Exhibit (h)(6)

                         EXPENSE LIMITATION UNDERTAKING

                             ALLIANCEBERNSTEIN L.P.
                          1345 Avenue of the Americas
                            New York, New York 10105

                                                October 15, 2013


AllianceBernstein Core Opportunities Fund, Inc.
1345 Avenue of the Americas
New York, New York 10105

Dear Sirs:

            AllianceBernstein L.P. herewith undertakes that for the Expense
Limitation Period, as defined below, we shall cause the aggregate operating
expenses of every character incurred by your AllianceBernstein Core
Opportunities Fund, Inc. (the "Fund") (but not including (i) extraordinary
expenses, (ii) interest expense, (iii) the fees and expenses of registered
investment companies or series thereof in which the Fund invests ("Acquired
Funds") other than investment advisory fees of Acquired Funds for which we serve
as investment adviser) to be limited to 1.20% in the case of the Class A shares,
1.90% in the case of the Class B shares and the Class C shares, .90% in the case
of the Advisor Class shares, 1.40% in the case of the Class R shares, 1.15% in
the case of Class K shares, .90% in the case of Class I shares, and .90% in the
case of Class Z shares, in each case of your aggregate average daily net assets
(the "Limitation"). To determine the amount of the Fund's expenses in excess of
the Limitation, the amount of allowable fiscal-year-to-date expenses shall be
computed daily by prorating the Limitation based on the number of days elapsed
within the fiscal year of the Fund (the "Prorated Limitation"). The Prorated
Limitation shall be compared to the expenses of the Fund recorded through the
current day in order to produce the allowable expenses to be recorded and
accrued for the Fund's current day (the "Allowable Expenses"). If the expenses
of the Fund for the current day exceed the Allowable Expenses, we shall be
responsible for such excess and will for the current day (i) reduce our advisory
fees and/or (ii) reimburse the Fund accordingly.

            For purposes of this Undertaking, the Expense Limitation Period
shall mean the period commencing on the date hereof and shall remain in effect
until the effective date of the next Post-Effective Amendment to the Fund's
Registration Statement on Form N-1A relating to the Fund (the "Registration
Statement") incorporating the Fund's financial statement. The Expense Limitation
Period and the Undertaking given hereunder will automatically be extended for
additional one-year periods unless we provide you with at least 60 days' notice
prior to the end of any Expense Limitation Period of our determination to modify
or to terminate this Undertaking at the end of its then current period.

            We understand and intend that you will rely on this Undertaking in
preparing and filing the Registration Statement with the Securities and Exchange
Commission, in accruing the Fund's expenses for purposes of calculating the
Fund's net asset value per share and for other purposes and expressly permit you
to do so.

                                                Very truly yours,

                                                ALLIANCEBERNSTEIN L.P.

                                                By:  /s/ Emilie D. Wrapp
                                                     -------------------
                                                     Emilie D. Wrapp
                                                     Assistant Secretary