SECURITIES AND EXCHANGE COMMISSION
                                    Washington, DC 20549

                                        SCHEDULE TO

                 Tender Offer Statement Under Section 14(d)(1) or 13(e)(1)
                           of the Securities Exchange Act of 1934

                           OFI Tremont Core Strategies Hedge Fund
                                      (Name of Issuer)

                           OFI Tremont Core Strategies Hedge Fund
                            (Name of Person(s) Filing Statement)

                               Shares of Beneficial Interest
                               (Title of Class of Securities)

                                         67084K103
                           (CUSIP Number of Class of Securities)

                                  Lisa I. Bloomberg, Esq.
                                 Two World Financial Center
                               225 Liberty Street, 11th Floor
                               New York, New York 10281-1008
                                       (212) 323-0560
            (Name, Address and Telephone Number of Person Authorized to Receive
          Notices and Communications on Behalf of the Person(s) Filing Statement)


                                 CALCULATION OF FILING FEE

-------------------------------------------------------------------------------
Transaction Valuation: $58,616,260.12a Amount of Filing Fee: $6,899.00b
-------------------------------------------------------------------------------

     (a)  Calculated  as the  estimated  aggregate  maximum  purchase  price for
twenty-five  percent of the Issuer's  outstanding shares of beneficial  interest
based on the estimated total net asset value of the Issuer's  outstanding shares
of beneficial interest as of November 30, 2005.

(b)  Calculated at 0.01177% of the Transaction Valuation.

     [ ] Check  the box if any part of the fee is  offset  as  provided  by Rule
0-11(a)(2)  and identify the filing with which the offsetting fee was previously
paid. Identify the previous filing by registration statement number, or the Form
or Schedule and the date of its filing.

Amount Previously Paid:
Form or Registration No.:
Filing Party:
Date Filed:

     [  ]  Check  the  box  if  the  filing   relates   solely  to   preliminary
communications made before the commencement of a tender offer.

     Check the  appropriate  boxes below to designate any  transactions to which
the statement relates:

  [  ]third-party tender offer subject to Rule 14d-1.
  [ x]issuer tender offer subject to Rule 13e-4.
  [  ]going-private transaction subject to Rule 13e-3.
  [  ]amendment to Schedule 13D under Rule 13d-2.

     Check the  following box if the filing is a final  amendment  reporting the
results of the tender offer: [ ]

ITEM 1:    SUMMARY TERM SHEET

     The  information  required by Item 1 is  incorporated  by  reference to the
Repurchase Offer Notice (Exhibit (a)(1)(ii)), which is attached as an exhibit to
this Schedule TO.

ITEM 2:    SUBJECT COMPANY INFORMATION

     There  is no  established  primary  or  secondary  trading  market  for the
securities.  As of  November  30,  2005,  the  number of  outstanding  shares of
beneficial interest of the Fund were 226,536.271.  Other information required by
Item 2 is  incorporated  by reference to the  Repurchase  Offer Notice  (Exhibit
(a)(1)(ii))  and the Repurchase  Request Form (Exhibit  (a)(1)(iii)),  which are
attached as Exhibits to this Schedule TO.

ITEM 3:    IDENTITY AND BACKGROUND OF FILING PERSON

     The name of the filing  person is OFI Tremont  Core  Strategies  Hedge Fund
(the "Fund"). The Fund's address is 6803 South Tucson Way, Centennial,  Colorado
80112, and the Fund's telephone number is 1.800.858.9826. The investment adviser
of the Fund is  OppenheimerFunds,  Inc., which is located at Two World Financial
Center, 225 Liberty Street,  New York, New York 10281-1008 (the "Adviser").  The
investment  manager is Tremont  Partners,  Inc.,  which is located at  Corporate
Center at Rye, Suite C-300, 555 Theodore Fremd Avenue,  Rye, New York 10580 (the
"Investment  Manager").  The distributor is OppenheimerFunds  Distributor,  Inc.
(the  "Distributor").  The Fund's  Independent  Trustees  are  Clayton  Yeutter,
Matthew Fink, Robert Galli, Phillip Griffiths, Mary Miller, Joel Motley, Kenneth
Randall,  Russell  Reynolds,  Joseph  Wikler,  Peter Wold and Brian Wruble.  The
Fund's  Interested  Trustee is John  Murphy.  The  Independent  Trustees and the
Interested  Trustee together form the "Board of Trustees".  The address for each
Trustee,  except  Mr.  Murphy,  is  6803 S.  Tucson  Way,  Centennial,  Colorado
80112-3924.  The  address  for Mr.  Murphy is Two World  Financial  Center,  225
Liberty Street, New York, New York 10281-1008.

ITEM 4:    TERMS OF THE REPURCHASE OFFER

     It is not  anticipated  that the Repurchase  Offer will be extended.  Other
information  required by Item 4 is  incorporated  by reference to the Repurchase
Offer Notice  (Exhibit  (a)(1)(ii))  and the  Repurchase  Request Form  (Exhibit
(a)(1)(iii)), which are attached as Exhibits to this Schedule TO.

ITEM 5:    PAST CONTRACTS, TRANSACTIONS, NEGOTIATIONS AND AGREEMENTS

Not Applicable.

ITEM 6:    PURPOSE OF TRANSACTION AND PLANS OR PROPOSALS OF THE FUND AND ITS AFFILIATES

     The  securities  acquired  in  the  transaction  will  be  retired.   Other
information  required by Item 6 is  incorporated  by reference to the Repurchase
Offer Notice  (Exhibit  (a)(1)(ii))  and the  Repurchase  Request Form  (Exhibit
(a)(1)(iii)), which are attached as Exhibits to this Schedule TO.

ITEM 7:    SOURCE AND AMOUNT OF FUNDS OR OTHER CONSIDERATIONS

     The  information  required by Item 7 is  incorporated  by  reference to the
Repurchase  Offer Notice (Exhibit  (a)(1)(ii))  and the Repurchase  Request Form
(Exhibit (a)(1)(iii)), which are attached as Exhibits to this Schedule TO.

ITEM 8:    INTEREST IN SECURITIES OF THE FUND

     As of November 30,  2005,  the Adviser is the  beneficial  owner of 111.186
shares (0.05%) of the Fund. Other information required by Item 8 is incorporated
by  reference  to the  Repurchase  Offer  Notice  (Exhibit  (a)(1)(ii))  and the
Repurchase Request Form (Exhibit (a)(1)(iii)), which are attached as Exhibits to
this Schedule TO.

ITEM 9:    PERSONS/ASSETS, RETAINED, EMPLOYED, COMPENSATED OR USED

     No persons have been  employed,  retained or are to be  compensated  by the
Fund to make  solicitations or recommendations in connection with the Repurchase
Offer.

ITEM 10:   FINANCIAL STATEMENTS

The following financial statements and information are incorporated by reference:

     (1) The Fund's audited  financial  statements  included in the Statement of
Additional Information,  dated July 29, 2005 for the fiscal year ended March 31,
2005 and filed on EDGAR on Form N-2 on July 29, 2005; and

     (2) The  annual  financial  statements,  previously  filed on EDGAR on Form
N-CSR on June 6, 2005, and the semi-annual financial statements previously filed
on EDGAR  Form  N-CSR on  November  29,  2005  which the Fund has  prepared  and
furnished to  Shareholders  pursuant to Rule 30e-1 under the Investment  Company
Act of 1940 and filed with the  Securities and Exchange  Commission  pursuant to
Rule 30e-1 under the Investment Company Act of 1940.

ITEM 11:   ADDITIONAL INFORMATION

(a)(1)      None.
(a)(2)      None.
(a)(3)      Not applicable.
(a)(4)      Not applicable.
(a)(5)      None.

(b)         None.

ITEM 12:   EXHIBITS

(a)(1)(i)  Cover Letter to Repurchase Offer.
(a)(1)(ii) Repurchase Offer Notice.
(a)(1)(iii) Form of Repurchase Request Form.
(a)(1)(iv) Form of Letter to Shareholders Regarding Acceptance of Tender of All Shares Held
            by Shareholders.
(a)(1)(v)  Form of Letter to Shareholders Regarding Acceptance of Tender of a Portion of
            Shares Held by Shareholders.
(a)(1)(vi) Form of Promissory Note for Payment Regarding Acceptance of Tender of All Shares
            Held by Shareholders.
(a)(1)(vii) Form of Promissory Note for Payment regarding Acceptance of Tender of a Portion
            of Shares Held by Shareholders.
(a)(2)      Not applicable.
(a)(3)      Not applicable.
(a)(4)      Not applicable.
(a)(5)      None.

(b)         Not applicable.

(d)         Not applicable.

(g)         None.

(h)         None.

ITEM 13:   INFORMATION REQUIRED BY SCHEDULE 13E-3

Not applicable.



                                         SIGNATURE

     After due inquiry  and to the best of my  knowledge  and belief,  I certify
that the information set forth in this statement is true, complete and correct.

                                    OFI Tremont Core Strategies Hedge Fund



                                    By: /s/ Lisa I. Bloomberg
                                    Name: Lisa I. Bloomberg
                                    Title:   Assistant Secretary

Date: January 31, 2006



Exhibit (a)(1)(i)

                           OFI Tremont Core Strategies Hedge Fund
                            Corporate Center at Rye, Suite C-300
                                 555 Theodore Fremd Avenue
                                    Rye, New York 10580

January 31, 2006

Dear OFI Tremont Core Strategies Hedge Fund Shareholder:

     OFI Tremont Core  Strategies  Hedge Fund is a  closed-end,  non-diversified
management  investment company organized as a business trust in the Commonwealth
of  Massachusetts  (the "Fund").  This notice is to inform you about your Fund's
offer to repurchase a portion of its outstanding  shares of beneficial  interest
("Shares") and to provide  instructions to Shareholders who would like to tender
some or all of their Shares for repurchase by the Fund. This Repurchase Offer is
intended to provide  liquidity to Shareholders  since Shares of the Fund are not
redeemable daily for cash nor are they traded on a stock exchange. You can offer
some  or all of  your  Shares  for  repurchase  only  during  one of the  Fund's
Repurchase Offers.

     The Repurchase Offer period will begin on February 1, 2006 and end on March
2, 2006. If you wish to sell any of your Shares during this tender  period,  you
can do so in one of the following ways:

     1. If your Shares are held in your own name  (please  refer to your account
statement),  you can complete the attached Repurchase Request Form and return it
to Tremont  Partners,  Inc. by 12:00  Midnight,  Eastern Time (ET),  on March 2,
2006.  The  Fund  currently  does  not  charge  a  processing  fee for  handling
repurchase requests.

     2. If your Shares are held for your retirement plan by your retirement plan
trustee,  your  retirement  plan trustee must submit the repurchase  request for
you. They may charge a transaction fee for that service.

     Please  refer to your Fund  Prospectus  and the enclosed  Repurchase  Offer
Notice and Repurchase  Request Form for more details.  If you are not interested
in selling any of your Shares at this time,  you do not have to do anything  and
can  disregard  this notice.  We will  contact you prior to the next  Repurchase
Offer.

     An Early  Withdrawal  Charge equal to 1.00% of the value of your Shares (or
portion thereof)  repurchased by the Fund will apply if the date as of which the
Shares  are to be  valued  for  purposes  of  repurchase  is less  than one year
following the date of your initial  investment in the Fund. If  applicable,  the
Early  Withdrawal  Charge will be deducted  before  payment of the proceeds of a
repurchase.


--------------------------------------------------------------------------------------------
All requests to have Shares  repurchased  must be received by Tremont  Partners,
Inc. at its office in Rye,  New York in good order no later than 12:00  Midnight
(ET),    on   March    2,    2006    (the    Repurchase    Request    Deadline).
--------------------------------------------------------------------------------------------

     Please refer to the enclosed  Repurchase Offer  documents.  If you have any
questions,  call your  financial  adviser  or  broker,  or you can call  Tremont
Partners, Inc. at 1.914.925.2951.

Sincerely,

Tremont Partners, Inc.


Exhibit (a)(1)(ii)

--------------------------------------------------------------------------------------------
                           OFI TREMONT CORE STRATEGIES HEDGE FUND
--------------------------------------------------------------------------------------------
--------------------------------------------------------------------------------------------
                                   6803 SOUTH TUCSON WAY
--------------------------------------------------------------------------------------------
                                 CENTENNIAL, COLORADO 80112
                                       1.800.858.9826
--------------------------------------------------------------------------------------------

--------------------------------------------------------------------------------------------
                                  REPURCHASE OFFER NOTICE
--------------------------------------------------------------------------------------------

--------------------------------------------------------------------------------------------
                     OFFER TO REPURCHASE SHARES OF BENEFICIAL INTEREST

                                      JANUARY 31, 2006

                       THE OFFER AND WITHDRAWAL RIGHTS WILL EXPIRE AT
                           12:00 MIDNIGHT (ET), ON MARCH 2, 2006
                                UNLESS THE OFFER IS EXTENDED

To the Shareholders of OFI Tremont Core Strategies Hedge Fund:

     OFI Tremont  Core  Strategies  Hedge Fund,  a  closed-end,  non-diversified
management  investment company organized as a business trust in the Commonwealth
of  Massachusetts  (the "Fund"),  is offering to  repurchase  up to  twenty-five
percent  (25%) of the aggregate  number of shares of beneficial  interest of the
Fund  ("Shares")  that are tendered by  Shareholders  and not withdrawn prior to
12:00 Midnight (ET), on March 2, 2006, subject to any extensions of the offer to
repurchase Shares ("Repurchase  Offer"). The amount due to any Shareholder whose
Shares are repurchased  will be equal to the value of the  Shareholder's  Shares
(or portion thereof being  repurchased)  determined as of March 31, 2006, or, if
the  Repurchase  Offer is extended,  as of a date  designated  by the Fund in an
amended notice to  Shareholders  (the  "Valuation  Date"),  and based on the net
asset  value of the  Fund's  assets as of that  date,  less an early  withdrawal
charge,  if  applicable.  Shareholders  may tender all,  or a portion of,  their
Shares up to an amount  such that they  maintain  the minimum  required  capital
account balance of $500,000 after the repurchase of Shares.

     Investors  should  realize  that the value of the Shares  tendered  in this
Repurchase Offer likely will change between December 30, 2005 (the last time net
asset value will have been calculated  before the start of this offer),  January
31, 2006,  February 28, 2006 (the next times net asset value will be calculated)
and March 31,  2006,  when the value of the Shares  tendered to the Fund will be
determined  for  purposes of  calculating  the  purchase  price of such  Shares.
Investors  should also realize that  although the  Repurchase  Offer  expires at
12:00 Midnight  (ET), on March 2, 2006, or, if the offer is extended,  such time
and dates as the Fund  designates  in an amended  notice to  Shareholders,  they
remain  Shareholders  in the Fund until the Valuation  Date. Any Shareholder who
wishes to obtain the most  recently  calculated  net asset value of their Shares
should contact Tremont Partners,  Inc. at 1.914.925.2951 during regular business
hours.

     Neither the Fund nor its Board of Trustees makes any  recommendation to any
Shareholder  whether to tender or refrain from  participating  in the Repurchase
Offer.  Each  Shareholder  must make an independent  decision  whether to tender
Shares and, if so, how many Shares to tender.

     No person has been authorized to make any  recommendation  on behalf of the
Fund whether  Shareholders  should tender pursuant to this Repurchase  Offer. No
person  has  been   authorized   to  give  any   information   or  to  make  any
representations  in  connection  with this  Repurchase  Offer  other  than those
contained in this Repurchase Offer or in the Fund's  Prospectus and Statement of
Additional  Information.  If  given or made,  any such  recommendation  and such
information  must not be relied upon as having been  authorized by the Fund, its
Investment Adviser, Distributor or Tremont Partners, Inc.

     This transaction has not been approved or disapproved by the Securities and
Exchange  Commission nor has the Securities and Exchange Commission or any state
securities  commission passed upon the fairness or merits of such transaction or
on the accuracy or adequacy of the information  contained in this document.  Any
representation to the contrary is unlawful.

     Questions and requests for assistance and requests for additional copies of
the  Repurchase  Offer may be directed  to Tremont  Partners,  Inc.,  the Fund's
Investment Manager, at 1.914.925.2951.



                                     SUMMARY TERM SHEET


     o OFI  Tremont  Core  Strategies  Hedge Fund (the  "Fund") is  offering  to
repurchase up to twenty-five  percent (25%) of the aggregate number of shares of
beneficial interest of the Fund ("Shares") that are tendered by Shareholders and
not withdrawn  prior to 12:00  Midnight  (ET), on March 2, 2006,  subject to any
extensions  of the  offer to  repurchase  Shares  ("Repurchase  Offer").  If the
Repurchase  Offer is  over-subscribed,  the Fund may repurchase  only a pro rata
portion of the shares tendered by each Shareholder. See Item 1 of the Repurchase
Offer Notice under "Formal Notice of Offer".

     o The Repurchase Offer will remain open until 12:00 Midnight (ET), on March
2, 2006, or if the Repurchase Offer is extended,  such time and date as the Fund
designates in an amended notice to Shareholders ("Repurchase Request Deadline").
Net asset value (that is, the value of the Fund's assets minus its  liabilities,
multiplied  by the  proportionate  shares in the Fund a  shareholder  desires to
tender) will be  calculated  for this  purpose as of March 31,  2006,  or if the
Repurchase Offer is extended,  as of a date designated by the Fund in an amended
notice  to  Shareholders  (the  "Valuation  Date").  See  Items  2 and 3 of  the
Repurchase Offer Notice.

     o Shareholders  must determine  whether to tender their Shares prior to the
Repurchase  Request  Deadline.  The net  asset  value  at which  the  Fund  will
repurchase Shares will not be calculated until the Valuation Date. The net asset
value can fluctuate  and may fluctuate  between the date you submit a Repurchase
Request and the Valuation  Date. The net asset value on the  Repurchase  Request
Deadline  and the  Valuation  Date could be higher or lower than on the date you
submit a Repurchase Request Form. See Item 4 of the Repurchase Offer Notice.

     o If the Fund accepts the tender of a Shareholder's  Shares,  then the Fund
will   give   the   Shareholder   either   cash  or  a   non-interest   bearing,
non-transferable  promissory note ("Promissory  Note") entitling the Shareholder
to  receive  an  amount  equal to the net  asset  value of the  Shares  tendered
determined  as  of  March  31,  2006.  The  Promissory  Note  will  entitle  the
Shareholder to receive an initial payment in cash and/or  marketable  securities
(where  determined to be  necessary)  equal to at least 95% of the unaudited net
asset value of the Shares  tendered by the  Shareholder  that are  accepted  for
purchase  by the  Fund  (the  "Initial  Payment")  which  will  be  paid  to the
Shareholder  no later than 45 days after the Valuation  Date or, if the Fund has
requested  withdrawals  of its capital from any hedge funds  ("Hedge  Funds") in
which the Fund  invests in order to fund the  purchase of Shares,  no later than
ten  business  days after the Fund has  received  at least 90% of the  aggregate
amount  withdrawn from such Hedge Funds.  The Promissory  Note will also entitle
the Shareholder to receive a contingent payment (the "Post Audit Payment") equal
to the excess,  if any, of (a) the net asset  value of the Shares  tendered  and
purchased as of the Valuation Date, as it may be adjusted based upon the results
of the  next  annual  audit of the  Fund's  financial  statements,  over (b) the
Initial  Payment.  The  Post  Audit  Payment  will be made  promptly  after  the
completion  of the Fund's annual audit for its fiscal year ending March 31, 2006
(which it expects will be completed 60 days after the fiscal year end). See Item
5 of the Repurchase Offer Notice.

     o An  Early  Withdrawal  Charge  equal to  1.00%  of the  value  of  Shares
repurchased  by the Fund will apply if the date as of which the Shares are to be
valued for purposes of  repurchase  is less than one year  following the date of
your initial investment in the Fund. If applicable,  the Early Withdrawal Charge
will be deducted before payment of the proceeds of a repurchase.  See Item 11 of
the Repurchase Offer Notice.

     o  Shareholders  who tender part of their Shares must leave an amount equal
to at least  $500,000 (the  "Required  Minimum  Balance") in the Fund.  The Fund
reserves  the right to reduce  the  amount  of  Shares  repurchased  so that the
Required  Minimum  Balance is  maintained.  See Item 7 of the  Repurchase  Offer
Notice.

     o Following  this summary is a formal notice of the Repurchase  Offer.  The
Repurchase Offer remains open until 12:00 Midnight (ET), on March 2, 2006. Until
this time,  Shareholders  have the right to change  their mind and may  withdraw
their Shares  submitted for  repurchase.  Shares  withdrawn may be  re-tendered,
however,  provided  that such  tenders  are made before the  Repurchase  Request
Deadline by following the tender procedures  described herein. See Item 8 of the
Repurchase Offer Notice.

     o  Shareholders  who would like the Fund to repurchase  all or a portion of
their  Shares  should  complete,  sign and send the  Repurchase  Request Form by
regular mail, certified mail, courier or express mail to Tremont Partners, Inc.,
c/o OFI Tremont  Core  Strategies  Hedge Fund,  Corporate  Center at Rye,  Suite
C-300, 555 Theodore Fremd Avenue, Rye, New York 10580, so long as it is received
before 12:00 Midnight (ET), on March 2, 2006. See Item 2 of the Repurchase Offer
Notice.

     o The value of Shares  may  change  between  February  1, 2006 and March 2,
2006.  The net asset  value of the  Shares is  calculated  by the Fund  based on
information  that  the  Fund  receives  from  the  Fund's  Investment   Manager.
Shareholders  may  obtain  the net asset  value of their  Shares  by  contacting
Tremont  Partners,  Inc. at  1.914.925.2951.  See Item 3 of the Repurchase Offer
Notice.

     o Shares  tendered  pursuant to the Repurchase  Offer may be withdrawn or a
Shareholder  may change the amount of Shares tendered for Repurchase at any time
prior to 12:00 Midnight (ET), on March 2, 2006. The Fund may suspend or postpone
this  Repurchase  Offer  only  by a  majority  vote  of the  Board  of  Trustees
(including a majority of the disinterested  Trustees).  Please note that just as
Shareholders have the right to withdraw their tendered Shares,  the Fund has the
right to cancel,  amend,  suspend or  postpone  this  Repurchase  Offer any time
before 12:00  Midnight  (ET),  on March 2, 2006.  Also realize that although the
tender offer  expires at 12:00  Midnight  (ET),  on March 2, 2006,  Shareholders
remain an investor in the Fund until March 31, 2006, when the net asset value of
a Shareholder's  Shares is calculated for purposes of determining the repurchase
price of the Shares. See Item 8 of the Repurchase Offer Notice.

     o It is the  responsibility  of each  Shareholder  who  elects to tender to
confirm receipt of the repurchase  request form with Tremont  Partners,  Inc. to
assure  good  delivery.  Please  send the  Repurchase  Request  Form to  Tremont
Partners, Inc. and not to your financial adviser.

                           FORMAL NOTICE OF THE REPURCHASE OFFER

     1. The Offer. The Fund is offering to repurchase up to twenty-five  percent
(25%) of the  aggregate  number  of shares of  beneficial  interest  of the Fund
("Shares")  at a price equal to the  respective  net asset value  ("NAV" or "Net
Asset Value") as of 12:00  Midnight (ET) on the Valuation  Date (defined  below)
upon the terms and conditions  set forth in this  Repurchase  Offer Notice,  the
Fund's  Prospectus,  and the related Repurchase  Request Form.  Together,  those
documents constitute the "Repurchase Offer." The purpose of the Repurchase Offer
is to  provide  liquidity  to  Shareholders  of  the  Fund.  The  offer  is  not
conditioned upon the tender for repurchase of any minimum amount of Shares.  The
Fund does not anticipate any extension of the Repurchase Offer.

     Shareholders may obtain the most recently calculated  information regarding
the Net Asset Value of their  Shares by  contacting  Tremont  Partners,  Inc. at
1.914.925.2951,  Monday through Friday, except holidays,  during normal business
hours of 9:00  a.m.  to 5:00 p.m.  (ET).  The value of the  Shares  tendered  by
Shareholders  likely will change  between  December  30, 2005 (the last time Net
Asset Value will have been calculated  before the start of this offer),  January
31,  2006 and  February  28,  2006 (the  next  times  Net  Asset  Value  will be
calculated) and March 31, 2006 when the value of the Shares tendered to the Fund
will be  determined  for  purposes of  calculating  the  purchase  price of such
Shares.

     The  repurchase of Shares  pursuant to the  Repurchase  Offer will have the
effect of decreasing the net assets of the Fund and increasing the proportionate
Shares in the Fund of Shareholders  who do not tender their Shares.  A reduction
in the net  assets  of the  Fund  could  limit  the  Fund's  access  to  certain
investment  opportunities,  cause the Fund to sell assets it would not have sold
otherwise  (including public  securities),  or result in Shareholders who do not
tender their  Shares  bearing  higher costs to the extent that certain  expenses
borne by the Fund are relatively  fixed and may not decrease if assets  decline.
The effects of decreased Fund size and the increased  proportionate Shares owned
by  Shareholders  who do not tender may be reduced or  eliminated  to the extent
that additional subscriptions for Shares are made from time to time.

     2. Repurchase  Request  Deadline - How to Submit  Requests.  All tenders of
Shares for  repurchase  must be received in proper  form (as  specified  in this
Repurchase Offer) by Tremont Partners, Inc. at its office in Rye, New York on or
before 12:00 Midnight (ET), on March 2, 2006.  Repurchase  Requests submitted to
Tremont  Partners,  Inc. in writing must be sent to the address specified in the
Repurchase  Request  Form.  Shareholders  wishing  to  confirm  receipt  of  the
Repurchase Request Form may contact Tremont Partners,  Inc. at 1.914.925.2951 or
at the address set forth in the Repurchase  Request Form. The method of delivery
of any  documents  is at the  election  and  complete  risk  of the  Shareholder
tendering  his or her  Shares,  including,  but not  limited  to, the failure of
Tremont  Partners,  Inc. to receive  the  Repurchase  Request  Form or any other
document.

     3. Valuation  Date.  Investors  should realize that the value of the Shares
tendered in this Offer  likely will change  between  December 30, 2005 (the last
time Net Asset Value will have been calculated  before the start of this offer),
January  31,  2006,  February  28,  2006 (the next times Net Asset Value will be
calculated)  and March 31, 2006 (the  "Valuation  Date"),  when the value of the
Shares  tendered to the Fund will be determined for purposes of calculating  the
purchase price of such Shares (unless the Repurchase Offer is extended,  then as
of a date  designated  by the Fund in an amended  notice to  Shareholders).  The
Fund's  estimated  unaudited Net Asset Value per share as of the dated indicated
below are:

                  January 2003            $1,011
                  February 2003           $1,016
                  March 2003              $1,022
                  April 2003              $1,037
                  May 2003                $1,044
                  June 2003               $1,048
                  July 2003               $1,049
                  August 2003             $1,048
                  September 2003          $1,059
                  October 2003            $1,058
                  November 2003           $1,061
                  December 2003           $1,022
                  January 2004            $1,030
                  February 2004           $1,034
                  March 2004              $1,037
                  April 2004              $1,032
                  May 2004                $1,028
                  June 2004               $1,029
                  July 2004               $1,026
                  August 2004             $1,023
                  September 2004          $1,029
                  October 2004            $1,035
                  November 2004           $1,061
                  December 2004           $1,012
                  January 2005            $1,004
                  February 2005           $1,017
                  March 2005              $1,008
                  April 2005                $985
                  May 2005                  $990
                  June 2005               $1,002
                  July 2005               $1,021
                  August 2005             $1,028
                  September 2005          $1,043
                  October 2005            $1,018
                  November 2005           $1,035

     As of the close of business on November 30, 2005, there were  approximately
226,536.271 Shares outstanding of the Fund.

     4. Net Asset Value. You must determine  whether to tender your Shares prior
to the Repurchase  Request  Deadline,  but the Net Asset Value at which the Fund
will repurchase  Shares will not be calculated until the Valuation Date. The Net
Asset Value can  fluctuate  and may  fluctuate  between the date you submit your
Repurchase  Request and the Repurchase  Request Deadline and the Valuation Date.
The Net Asset Value on the  Repurchase  Request  Deadline and the Valuation Date
could be  higher  or lower  than on the date you  submit a  Repurchase  Request.
Shareholders may obtain the most recently calculated  information  regarding the
Net  Asset  Value of their  Shares  by  contacting  Tremont  Partners,  Inc.  at
1.914.925.2951,  Monday through Friday, except holidays,  during normal business
hours of 9:00 a.m. to 5:00 p.m. (ET).

     5.  Payment for  Repurchased  Shares.  If all Shares of a  Shareholder  are
repurchased, the Shareholder will receive an initial payment equal to 95% of the
estimated  value of the Shares and the balance due will be  determined  and paid
promptly  after  completion  of  the  Fund's  audit  and  be  subject  to  audit
adjustment.  The total  amount that a  Shareholder  may expect to receive on the
repurchase of the Shareholder's Shares (or portion thereof) will be the value of
the Shareholder's  Shares (or portion thereof being  repurchased)  determined on
the  Valuation  Date and based on the Net Asset Value of the Fund's assets as of
that date, minus any Early Withdrawal Charge, if applicable. This amount will be
subject  to  adjustment  upon  completion  of the  annual  audit  of the  Fund's
financial  statements  for the fiscal year in which the  repurchase  is effected
(which it is  expected  will be  completed  within 60 days after the end of each
fiscal year).

     If the Fund  accepts the tender of a  Shareholder's  Shares,  then the Fund
will   give   the   Shareholder   either   cash  or  a   non-interest   bearing,
non-transferable  promissory note ("Promissory  Note") entitling the Shareholder
to  receive  an  amount  equal to the net  asset  value of the  Shares  tendered
determined  as  of  March  31,  2006.  The  Promissory  Note  will  entitle  the
Shareholder to receive an initial payment in cash and/or  marketable  securities
(where  determined to be  necessary)  equal to at least 95% of the unaudited net
asset value of the Shares  tendered by the  Shareholder  that are  accepted  for
purchase  by the  Fund  (the  "Initial  Payment")  which  will  be  paid  to the
Shareholder  no later than 45 days after the Valuation  Date or, if the Fund has
requested withdrawals of its capital from any hedge fund ("Hedge Fund") in which
the Fund  invests in order to fund the  purchase  of  Shares,  no later than ten
business days after the Fund has received at least 90% of the  aggregate  amount
withdrawn  from such Hedge  Funds.  The  Promissory  Note will also  entitle the
Shareholder to receive a contingent  payment (the "Post Audit Payment") equal to
the  excess,  if any,  of (a) the net asset  value of the  Shares  tendered  and
purchased as of the Valuation Date, as it may be adjusted based upon the results
of the  next  annual  audit of the  Fund's  financial  statements,  over (b) the
Initial  Payment.  The  Post  Audit  Payment  will be made  promptly  after  the
completion  of the Fund's annual audit for its fiscal year ending March 31, 2006
(which it expects will be completed 60 days after the fiscal year end).

     6.  Increase  in Amount of Shares  Repurchased;  Pro Rata  Repurchases.  If
Shareholders  tender for  repurchase  more  outstanding  Shares than the Fund is
offering  to  repurchase  during  the  offering  period,  the Fund  may,  in the
discretion  of the Board of Trustees  (but is not  obligated  to)  increase  the
outstanding  Shares  that the Fund is  offering to purchase by up to two percent
(2%) on the Repurchase Request Deadline.  If the outstanding Shares tendered for
repurchase  exceed the amount that the Fund is offering to repurchase,  the Fund
will  repurchase  only  a pro  rata  portion  of the  Shares  tendered  by  each
Shareholder.  There can be no assurance that the Fund will be able to repurchase
all the Shares  that you tender  even if you tender all the Shares that you own.
In the  event  of an  oversubscribed  Repurchase  Offer,  you may be  unable  to
liquidate  some or all of your Shares at Net Asset  Value.  You may have to wait
until a  subsequent  Repurchase  Offer to tender  the  Shares  that the Fund was
unable to  repurchase,  and you would be subject to the risk of Net Asset  Value
fluctuations during that time.

     7.  Amount of  Tender.  Shareholders  may  tender all or a portion of their
Shares. In addition,  a Shareholder who tenders for repurchase only a portion of
its Shares will be required  to maintain a minimum  account  balance of $500,000
that is to be debited  from the account of the  Shareholder  as of the date that
the Fund  values the  Shares for  repurchase.  The Fund  maintains  the right to
reduce the portion of Shares to be  repurchased  from a Shareholder  so that the
required  minimum account  balance is maintained.  The Fund will promptly notify
the  Shareholder if the tender of a portion of the Shares for  repurchase  would
reduce such shareholder's account balance to less than $500,000.

     The Fund may redeem all or part of a  Shareholder's  Shares if, among other
reasons,  the Adviser  determines  that it would be in the best interests of the
Fund to do so. The Fund  reserves the right to reduce that portion of the Shares
to be purchased from a Shareholder to maintain the Shareholder's account balance
at $500,000 if a Shareholder  tenders a portion of his Shares and the repurchase
of that portion would cause the Shareholder's account balance to fall below this
required minimum.

     8. Withdrawal of Tender of Shares for Repurchase.  Shares tendered pursuant
to the  Repurchase  Offer may be withdrawn or the amount of Shares  tendered for
Repurchase  may be changed at any time prior to 12:00 Midnight (ET), on March 2,
2006 (the  "Repurchase  Request  Deadline").  You must send a written  notice to
Tremont Partners,  Inc. at the address specified in this Repurchase Request Form
or the  Prospectus,  and  Tremont  Partners,  Inc.  must  receive  it before the
Repurchase  Request  Deadline.  All  questions  as  to  the  form  and  validity
(including  time of receipt) of a notice of withdrawal will be determined by the
Fund, in its sole discretion, and such determination shall be final and binding.
Shares  properly  withdrawn  shall not  thereafter  be deemed to be tendered for
purposes of the Repurchase Offer.  However,  withdrawn Shares may be re-tendered
prior to the Repurchase  Request Deadline by following the procedures  described
herein.  In addition,  Shares tendered  pursuant to the Repurchase  Offer may be
withdrawn if not yet accepted for payment  after the  expiration of 40 days from
the commencement of the Repurchase Offer.

     9. Suspension or Postponement of Repurchase Offer. The Board of Trustees of
the Fund may suspend or postpone this  Repurchase  Offer only by a majority vote
of the Trustees (including a majority of the disinterested Trustees) and only:

     (A) for any period  during which The New York Stock  Exchange or any market
in which the  securities  owned by the Fund are  principally  traded is  closed,
other than customary  weekend and holiday  closings,  or during which trading in
such market is restricted;

     (B) for any period  during which an  emergency  exists as a result of which
disposal by the Fund of securities owned by it is not reasonably practicable, or
during which it is not reasonably  practicable  for the Fund fairly to determine
the value of its net assets; or

     (C) for such other periods as the  Securities  and Exchange  Commission may
order for the protection of Shareholders of the Fund.

     10. Tax  Consequences.  A tender of Shares pursuant to the Repurchase Offer
will be  treated as a taxable  sale of the  Shares if the tender (i)  completely
terminates  the  Shareholder's  interest in the Fund,  (ii) is treated under the
Internal Revenue Code as a distribution that is "substantially disproportionate"
or (iii) is treated under the Internal  Revenue Code as a  distribution  that is
"not essentially equivalent to a dividend".  A "substantially  disproportionate"
distribution generally requires a reduction of at least 20% in the Shareholder's
proportionate interest in the Fund after all Shares are tendered. A distribution
"not essentially  equivalent to a dividend" requires that there be a "meaningful
reduction"  in the  Shareholder's  interest,  which  should  be the  case if the
Shareholder has a minimal  interest in the Fund,  exercises no control over Fund
affairs and suffers a reduction in his or her proportionate  interest.  The Fund
intends to take the position that tendering  Shareholders  will qualify for sale
treatment. If the transaction is treated as a sale for tax purposes, any gain or
loss recognized  will be treated as a capital gain or loss by  Shareholders  who
hold their Shares as a capital asset and as a long-term  capital gain or loss if
such Shares have been held for more than twelve  months.  If the  transaction is
not treated as a sale, the amount  received upon a sale of Shares may consist in
whole or in part of  ordinary  dividend  income,  a return of capital or capital
gain,  depending on the Fund's earnings and profits for its taxable year and the
Shareholder's  basis in the Shares.  In  addition,  if any amounts  received are
treated as a dividend to tendering Shareholders,  a constructive dividend may be
received by non-tendering  Shareholders whose proportionate interest in the Fund
has been increased as a result of the tender.

     Shareholders  should consult their tax advisers  regarding the specific tax
consequences,  including  state and local tax  consequences,  of a repurchase of
their Shares. Special tax rules apply to Shares repurchased from retirement plan
accounts.

     11. Early Withdrawal  Charges.  The Fund does not charge a special handling
or processing fee for repurchases.  However, if you tender for repurchase Shares
that  are  subject  to Early  Withdrawal  Charges  as  described  in the  Fund's
Prospectus,  and if those Shares are  repurchased  by the Fund,  the  applicable
Early Withdrawal  Charge will be deducted from the proceeds of the repurchase of
your Shares.  If you ask the Fund to repurchase a specific dollar amount of your
Shares,  and if the  Shares  are  subject  to  Early  Withdrawal  charges,  then
(assuming your request is not subject to pro-ration) the Fund will repurchase an
amount  sufficient  to pay  the net  proceeds  you  have  requested  and  enough
additional Shares to pay the applicable Early Withdrawal Charge.

     12. Proper Form of Repurchase  Request  Documents.  All questions as to the
validity,  form, eligibility  (including,  for example, the time of receipt) and
acceptance  of  repurchase  requests will be determined by the Fund, in its sole
discretion,  and that determination will be final and binding. The Fund reserves
the right to reject  any and all  tenders  of  repurchase  requests  for  Shares
determined  not to be in the proper form, or to refuse to accept for  repurchase
any Shares if, in the  opinion  of counsel to the Fund,  paying for such  Shares
would be unlawful. The Fund also reserves the absolute right to waive any of the
conditions  of this  Repurchase  Offer or any  defect in any  tender of  Shares,
whether in general or with respect to any particular Shares or Shareholders. The
Fund's  interpretations  of the terms and  conditions of this  Repurchase  Offer
shall be final and binding.  Unless  waived,  any defects or  irregularities  in
connection with  repurchase  requests must be cured within the times as the Fund
shall  determine.  Tenders of Shares  will not be deemed to have been made until
all defects or irregularities have been cured or waived.

     Neither the Fund, Tremont Partners,  Inc. (the Fund's Investment  Manager),
OppenheimerFunds,  Inc. (the Fund's Investment  Adviser),  nor  OppenheimerFunds
Distributor,  Inc. (the Fund's Distributor),  nor any other person is or will be
obligated to give notice of any defects or irregularities in repurchase requests
tendered, nor shall any of them incur any liability for failure to give any such
notice.

     13. Certain Information About the Fund. The Fund does not have any plans or
proposals  that relate to or would result in: (a) the  acquisition by any person
of additional  Shares (other than the Fund's  intention to accept  subscriptions
for Shares from time to time in the  discretion of the Fund) or the  disposition
of Shares,  other than as  disclosed  in the  Prospectus;  (b) an  extraordinary
transaction,  such as a merger,  reorganization  or  liquidation,  involving the
Fund; (c) any material change in the present distribution policy or indebtedness
or  capitalization of the Fund; (d) any change in the identity of the Investment
Manager, Investment Adviser or Trustees of the Fund, or in the management of the
Fund including,  but not limited to, any plans or proposals to change the number
or term of the Trustees of the Fund, to fill any existing  vacancy for a Trustee
of  the  Fund  or to  change  any  material  term  of  the  investment  advisory
arrangements with the Investment  Adviser;  (e) a sale or transfer of a material
amount  of assets  of the Fund  (other  than as the  Trustees  determine  may be
necessary or appropriate to fund any portion of the repurchase  price for Shares
acquired  pursuant to this  Repurchase  Offer or in connection with the ordinary
portfolio transactions of the Fund); (f) any other material change in the Fund's
structure or business,  including  any plans or proposals to make any changes in
its fundamental  investment policy for which a vote would be required by Section
13 of the Investment  Company Act of 1940; or (g) any changes in the Declaration
of Trust or other actions that may impede the acquisition of control of the Fund
by any person.

     During the past 60 days,  other than the acceptance of purchases for Shares
in December  2005,  no  transactions  involving  the Shares were effected by the
Fund, the Investment Manager, Investment Adviser or Trustees of the Fund, or any
person controlling either the Fund or the Investment Manager, Investment Adviser
or any Trustees of the Fund.

     14.  Miscellaneous.  The  Repurchase  Offer is not being  made to, nor will
tenders  be  accepted  from,  Shareholders  in any  jurisdiction  in  which  the
Repurchase  Offer or its acceptance would not comply with the securities or Blue
Sky  laws  of  such  jurisdiction.  The  Fund  reserves  the  right  to  exclude
Shareholders  from  the  Repurchase  Offer  in any  jurisdiction  in which it is
asserted that the  Repurchase  Offer cannot  lawfully be made. The Fund believes
that such  exclusion  is  permissible  under  applicable  laws and  regulations,
provided  the Fund makes a good faith effort to comply with any state law deemed
applicable to the Repurchase Offer.

     Neither the Fund nor its Board of Trustees makes any  recommendation to any
Shareholder  whether to tender or refrain from  participating  in the Repurchase
Offer.  Each  Shareholder  must make an independent  decision  whether to tender
Shares and, if so, how many Shares to tender.

     No person has been authorized to make any  recommendation  on behalf of the
Fund whether  Shareholders  should tender pursuant to this Repurchase  Offer. No
person  has  been   authorized   to  give  any   information   or  to  make  any
representations  in  connection  with this  Repurchase  Offer  other  than those
contained in this Repurchase Offer or in the Fund's  Prospectus and Statement of
Additional  Information.  If  given or made,  any such  recommendation  and such
information  must not be relied upon as having been  authorized by the Fund, its
Investment Adviser, Distributor or Tremont Partners, Inc.

     This transaction has not been approved or disapproved by the Securities and
Exchange  Commission nor has the Securities and Exchange Commission or any state
securities  commission passed upon the fairness or merits of such transaction or
on the accuracy or adequacy of the information  contained in this document.  Any
representation to the contrary is unlawful.

     For the Fund's  current  Net Asset Value and other  information  about this
Repurchase Offer, or for a copy of the Fund's Prospectus, call Tremont Partners,
Inc. at 1.914.925.2951 or contact your financial adviser.


Dated:  January 31, 2006

Tremont Partners, Inc.


Exhibit (a)(1)(iii)

                              FORM OF REPURCHASE REQUEST FORM

--------------------------------------------------------------------------------------------
                           OFI TREMONT CORE STRATEGIES HEDGE FUND
--------------------------------------------------------------------------------------------
                                  REPURCHASE REQUEST FORM

To: OFI Tremont Core Strategies Hedge Fund

     Please  repurchase  the Shares of OFI Tremont  Core  Strategies  Hedge Fund
designated  below on the Valuation  Date that applies to this  Repurchase  Offer
which expires on March 2, 2006. I understand  that if my repurchased  Shares are
subject to an Early  Withdrawal  Charge,  that charge will be deducted  from the
proceeds of my repurchased Shares.

---------------------------------------------------------------------------------
Name(s) of Registered Shareholders:
(Please fill in EXACTLY as listed
on your Fund statement):
---------------------------------------------------------------------------------
---------------------------------------------------------------------------------
Your Account Number:
(Please fill in EXACTLY as listed
on your Fund statement):
---------------------------------------------------------------------------------
---------------------------------------------------------------------------------
Your Daytime Telephone Number:       Area Code: (         ) Telephone No.:
---------------------------------------------------------------------------------

Shares Tendered for Repurchase:
(Please fill in ALL applicable information):
---------------------------------------------------------------------------------
|_|  Full Tender    Please tender all of my Shares.
---------------------------------------------------------------------------------
---------------------------------------------------------------------------------
|_|  Partial Tender Please tender all but $________________ of my Shares
                    (Please Note: A $500,000 minimum balance must be retained.)
---------------------------------------------------------------------------------
---------------------------------------------------------------------------------
                    Please repurchase enough of my Shares so that I will
                    receive $___________________.
                    (If an Early Withdrawal Charge applies, enough of my Shares
|_|  Dollar Amount  will be repurchased, subject to pro-ration, to provide the
                    net proceeds requested. Please Note: A $500,000 minimum
                    account balance must be retained.)
---------------------------------------------------------------------------------

Payment and Delivery Instructions:

     The  proceeds  of  repurchased  Shares  will be  wired  to you per the wire
instructions  that you provide  below.  Your  signature(s)  on this form must be
guaranteed per the instructions on the following page. A confirming  e-mail will
be sent to you when the proceeds of the repurchased shares are wired.

Wiring Instructions:    Bank Name:        __________________________________
                  ABA#:             __________________________________
                  Account Name:           __________________________________
                  Account #:        __________________________________
                  For Further Credit To:  __________________________________


PLEASE ASSURE THAT YOU SIGN THIS FORM WHERE INDICATED!

Please sign below and note the following important points:

o     Your  signature(s)  below MUST  CORRESPOND  EXACTLY  with the  names(s)  in which your
       Shares are registered.
o     If the Shares are held by two or more joint holders, ALL SHAREHOLDERS MUST SIGN BELOW.
o     If the Shares are held in a 403(b)(7) account,  you must have the custodian submit the
       request on your behalf.
o     If  the   Shares   are  held  in  the   name  of  a   trustee,   executor,   guardian,
       attorney-in-fact,  corporation, partnership or other representative capacity, include
       the name of the owner,  sign using your title and submit  evidence of your  authority
       in a form satisfactory to Tremont Partners, Inc.

     ALL signatures must be guaranteed by one of the following: U.S. bank, trust
company,  credit union or savings  association,  or by a foreign bank that has a
U.S. correspondent bank, or by a U.S. registered dealer or broker in securities,
municipal securities, or government securities, or by a U.S. national securities
exchange, a registered securities association or a clearing agency.

Date:_______________________________            Signatures(s) of owner(s)
                                          exactly as Shares are registered:
SIGNATURE(s) GUARANTEED BY:


____________________________________            _____________________________________
(Signature)                                     (Signature of Owner)


____________________________________            _____________________________________
(Name)  (Title)                                 (Signature of Joint Owner)

     If you have any questions about this form, call Tremont  Partners,  Inc. at
1.914.925.2951.

     This form must be received by Tremont  Partners,  Inc. by 12:00 Midnight ET
March 2, 2006 (the Repurchase Request Deadline), if you want to sell some or all
of your  account of the OFI  Tremont  Core  Strategies  Hedge  Fund.  Repurchase
requests  received  by  Tremont  Partners,  Inc.  cannot  be  revoked  after the
repurchase request deadline.

               -------------------------------------------------------
                  SEND THIS FORM BY REGULAR MAIL, EXPRESS MAIL OR
                               OVERNIGHT COURIER TO:
                               Tremont Partners, Inc.
                      c/o OFI Institutional Hedge Fund Series
                        Corporate Center at Rye, Suite C-300
                             555 Theodore Fremd Avenue
                                Rye, New York 10580
                             Attention: Jhonny Quiroga
               -------------------------------------------------------

     Neither the Fund nor its Board of Trustees makes any  recommendation to any
Shareholder  whether to tender or refrain from  participating  in the Repurchase
Offer.  Each  Shareholder  must make an independent  decision  whether to tender
Shares and, if so, how many Shares to tender.

     No person has been authorized to make any  recommendation  on behalf of the
Fund whether  shareholders  should tender pursuant to this Repurchase  Offer. No
person  has  been   authorized   to  give  any   information   or  to  make  any
representations  in  connection  with this  Repurchase  Offer  other  than those
contained in this Repurchase Offer or in the Fund's  Prospectus and Statement of
Additional  Information.  If  given or made,  any such  recommendation  and such
information  must not be relied upon as having been  authorized by the Fund, its
Investment Adviser, Distributor or Tremont Partners, Inc.

     This transaction has not been approved or disapproved by the Securities and
Exchange  Commission nor has the Securities and Exchange Commission or any state
securities  commission passed upon the fairness or merits of such transaction or
on the accuracy or adequacy of the information  contained in this document.  Any
representation to the contrary is unlawful.


Exhibit (a)(1)(iv)



FORM OF LETTER TO SHAREHOLDERS REGARDING ACCEPTANCE OF TENDER OF ALL SHARES HELD
                          BY SHAREHOLDER


Date: __________


Dear Shareholder:

     OFI  Tremont  Core  Strategies  Hedge Fund (the  "Fund") has  received  and
accepted for purchase your tender of your Shares in the Fund.

     Because  you  have  tendered  and  the  Fund  has  purchased   your  entire
investment,  you have been paid a note (the "Note")  entitling you to receive an
initial payment of 95% of the estimated  repurchase price based on the unaudited
net asset value of the Fund as of March 31, 2006 (the "Valuation  Date"),  after
subtraction of any applicable charges, including a 1.00% Early Withdrawal Charge
that applies if the date as of which the Shares are to be valued for purposes of
the  repurchase  is less  than  one  year  following  the  date of your  initial
investment in the Fund, in accordance  with the terms of the  Repurchase  Offer.
You will  receive an initial  payment in this  amount via wire or check,  as per
your instructions on your Repurchase  Request Form. In accordance with the terms
of the Repurchase Offer, payment will be made within forty-five (45) days of the
Valuation  Date unless the Fund has  requested a withdrawal  of its capital from
any Hedge  Fund(s)  in order to fund the  repurchase  of  Shares,  in which case
payment will be made ten (10) business days after the Fund has received at least
90% of the aggregate amount withdrawn by the Fund from such Hedge Funds.

     The terms of the Note provide that a contingent  payment  representing  the
balance of the purchase  price,  if any, will be paid to you promptly  after the
completion of the Fund's March 31, 2006 fiscal  year-end audit and is subject to
fiscal year-end audit  adjustment.  This amount will be paid to you via wire, as
per your instructions on your Repurchase Request Form. We expect the audit to be
completed by the end of May 2006.

     The Note is held by Tremont  Partners,  Inc. on your behalf for your safety
and  convenience.  Once  payment has been made to you in full under the terms of
the Note, the Note will be cancelled.

     Should  you have any  questions,  please  call your  financial  adviser  or
broker, or you can call Tremont Partners, Inc. at 1.914.925.2951.

Sincerely,


Tremont Partners, Inc.



Exhibit (a)(1)(v)


FORM OF LETTER TO SHAREHOLERS REGARDING ACCEPTANCE OF TENDER OF A PORTION OF
                         SHARES HELD BY SHAREHOLDER


Date: _____________

Dear Shareholder:

     OFI  Tremont  Core  Strategies  Hedge Fund (the  "Fund") has  received  and
accepted for purchase your tender of a portion of your Shares in the Fund.

     Because  you have  tendered  and the Fund has  purchased  a portion of your
investment,  you have been paid a note (the  "Note")  entitling  you to  receive
payment of 100% of the  estimated  repurchase  price based on the  unaudited net
asset  value of the Fund as of March 31,  2006  (the  "Valuation  Date"),  after
subtraction  of any  applicable  charges,  including the 1.00% Early  Withdrawal
Charge  that  applies  if the date as of which the  Shares  are to be valued for
purposes  of the  repurchase  is less than one year  following  the date of your
initial  investment in the Fund, in accordance  with the terms of the Repurchase
Offer.  You will receive a payment in this amount via wire or check, as per your
instructions  on your  Repurchase  Request Form. In accordance with the terms of
the Repurchase  Offer,  payment will be made within  forty-five (45) days of the
Valuation  Date unless the Fund has  requested a withdrawal  of its capital from
any Hedge Funds in order to fund the repurchase of Shares, in which case payment
will be made ten (10)  business days after the Fund has received at least 90% of
the aggregate amount withdrawn by the Fund from such Hedge Funds.

     The Note is held by Tremont  Partners,  Inc. on your behalf for your safety
and  convenience.  Once  payment has been made to you in full under the terms of
the Note, the Note will be cancelled.

     You remain a  Shareholder  of the Fund with  respect to the portion of your
Shares in the Fund that you did not tender.

     Should  you have any  questions,  please  call your  financial  adviser  or
broker, or you can call Tremont Partners, Inc. at 1.914.925.2951.

Sincerely,


Tremont Partners, Inc.


Exhibit (a)(1)(vi)

FORM OF PROMISSORY NOTE FOR PAYMENT REGARDING ACCEPTANCE OF TENDER OF ALL SHARES
                           HELD BY SHAREHOLDER

     Pursuant  to  the  Offer  to  Purchase  (the  "Repurchase   Offer")  up  to
twenty-five  percent  (25%)  of  the  Fund's  aggregate  outstanding  shares  of
beneficial  interest  ("Shares")  at a price equal to the net asset value on the
Valuation Date upon the terms and conditions set forth in the Repurchase  Offer,
OFI Tremont Core  Strategies  Hedge Fund hereby  promises to pay in cash, in the
manner  set forth  below,  to the  person  identified  below as the  payee  (the
"Payee")  an  amount  equal to the  estimated  net  asset  value  of the  Shares
tendered,  determined  as of the  Valuation  Date in  accordance  with the asset
valuation policy of the Fund.

     This note  entitles  the Payee to  receive an  initial  payment,  valued in
accordance with the terms of the Repurchase Offer,  equal to at least 95% of the
estimated value of the Shares (the "Initial  Payment") which will be paid to the
payee in the form of a wire  within  forty-five  (45) days  after the  Valuation
Date,  unless the Fund has  requested a withdrawal of its capital from any Hedge
Fund(s) in order to fund the repurchase of Shares, in which case payment will be
made ten (10)  business  days  after the Fund has  received  at least 90% of the
aggregate  amount  withdrawn  by the Fund  from  such  Hedge  Fund(s).  An Early
Withdrawal  Charge  of 1.00% of the  value of  Shares  (or  portion  of  Shares)
repurchased  by the Fund will apply if the date as of which the Shares are to be
valued for purposes of  repurchase  is less than one year  following the date of
the Payee's initial investment in the Fund. If applicable,  the Early Withdrawal
Charge will be deducted before payment of the proceeds of a repurchase.

     This note also  entitles  the Payee to a  contingent  payment  equal to the
excess,  if any, of (x) the net asset  value of the Shares (or portion  thereof)
repurchased by the Fund as of the date of such  repurchase,  determined based on
the audited  financial  statements of the Fund for the Fiscal Year in which such
repurchase was effective over (y) the Initial Payment. The contingent payment is
payable  promptly  after the  completion  of the audit of the  Fund's  financial
statements for the fiscal year ending March 31, 2006.

     Both the initial and contingent  payments  hereunder shall be paid in cash,
provided,  however, that if the Fund's Board of Trustees determines that payment
of all or a  portion  of the  purchase  price by a  distribution  of  marketable
securities  is  necessary  to  avoid  or  mitigate  any  adverse  effect  of the
Repurchase  Offer on the remaining  Shareholders  of the Fund, then such payment
shall be made by  distributing  such  marketable  securities,  all as more fully
described in the Repurchase Offer.

     Both the initial and contingent  payment of this note shall be made by wire
to the Payee, as per the Payee's instruction on the Repurchase Request Form.

This note may not be pledged, assigned or otherwise transferred by the Payee.

     This note shall be  construed  according to and governed by the laws of the
State of New York  without  giving  effect to the  conflict  of laws  principles
thereof.  Any capitalized term used herein but not defined herein shall have the
meaning ascribed to it in the Repurchase Offer.

Payee: _______________________
                                         OFI Tremont Core Strategies Hedge Fund

                                         By: _______________________________


Exhibit (a)(1)(vii)

FORM OF PROMISSORY NOTE FOR PAYMENT REGARDING ACCEPTANCE OF TENDER OF A PORTION
                          OF SHARES HELD BY SHAREHOLDER

     Pursuant  to  the  Offer  to  Purchase  (the  "Repurchase   Offer")  up  to
twenty-five  percent  (25%)  of  the  Fund's  aggregate  outstanding  shares  of
beneficial  interest  ("Shares")  at a price equal to the net asset value on the
Valuation Date upon the terms and conditions set forth in the Repurchase  Offer,
OFI Tremont Core  Strategies  Hedge Fund hereby  promises to pay in cash, in the
manner  set forth  below,  to the  person  identified  below as the  payee  (the
"Payee")  an  amount  equal to the  estimated  net  asset  value  of the  Shares
tendered,  determined  as of the  Valuation  Date in  accordance  with the asset
valuation policy of the Fund.

     This Note  entitles  the Payee to receive a payment,  valued in  accordance
with the terms of the Repurchase Offer,  equal to 100% of the estimated value of
the Shares which will be paid to the payee in the form of a check or wire within
forty-five (45) days after the Valuation  Date,  unless the Fund has requested a
withdrawal of its capital from any Hedge Fund(s) in order to fund the repurchase
of Shares,  in which case payment will be made ten (10)  business days after the
Fund has  received at least 90% of the  aggregate  amount  withdrawn by the Fund
from such Hedge  Fund(s).  An Early  Withdrawal  Charge of 1.00% of the value of
Shares (or portion of Shares)  repurchased by the Fund will apply if the date as
of which the Shares are to be valued for purposes of repurchase is less than one
year  following  the date of the  Payee's  initial  investment  in the Fund.  If
applicable,  the Early Withdrawal  Charge will be deducted before payment of the
proceeds of a repurchase.

     The payment hereunder shall be paid in cash, provided, however, that if the
Fund's  Board of  Trustees  determines  that  payment of all or a portion of the
purchase price by a distribution of marketable  securities is necessary to avoid
or  mitigate  any  adverse  effect  of the  Repurchase  Offer  on the  remaining
Shareholders of the Fund,  then such payment shall be made by distributing  such
marketable securities, all as more fully described in the Repurchase Offer.

     The  payment of this Note  shall be made by wire to the  Payee,  as per the
Payee's instruction on the Repurchase Request Form.

This Note may not be pledged, assigned or otherwise transferred by the Payee.

     This Note shall be  construed  according to and governed by the laws of the
State of New York  without  giving  effect to the  conflict  of laws  principles
thereof.

     Any  capitalized  term used  herein but not defined  herein  shall have the
meaning ascribed to it in the Repurchase Offer.

Payee: _______________________

                                    OFI Tremont Core Strategies Hedge Fund


                                    By: _______________________________