PROSPECTUS Dated May 1, 1996                      Pricing Supplement No. 34 to
PROSPECTUS SUPPLEMENT                     Registration Statement No. 333-01655
Dated May 1, 1996                                              August 21, 1996
                                                                Rule 424(b)(3)

                           Morgan Stanley Group Inc.
                          MEDIUM-TERM NOTES, SERIES C
                          Senior Floating Rate Notes



     The Medium-Term Notes, Series C (Senior Floating Rate Notes) described in
this Pricing Supplement (the "Notes") will mature on the Maturity Date and
will not be redeemable at the option of Morgan Stanley Group Inc. prior to the
Maturity Date.  The Notes are further described under "Description of Notes --
Floating Rate Notes" in the accompanying Prospectus Supplement, except that to
the extent the terms described below are inconsistent with such description,
the terms described below shall control.

                      
Principal Amount:      $15,000,000

Maturity Date:         August 26, 1997; provided that if such day is not a Business Day, the payment
                       of principal and interest will be made on the next succeeding Business Day,
                       and no interest on such payment shall accrue for the period from and after the
                       Maturity Date

Interest Accrual
  Date:                August 30, 1996


Interest Payment
  Dates:               The twenty-sixth day of each month, commencing September 26, 1996. If any such
                       day (other than the Maturity Date) is not a Business Day, such Interest
                       Payment Date will be the next succeeding Business Day, except that if such
                       Business Day is in the next succeeding calendar month, such Interest Payment
                       Date shall be the next preceding day that is a Business Day

Initial Interest Rate: 5.36625%

Base Rate:             LIBOR

Index Maturity:        1 Month

Spread (Plus or
  Minus):              Minus 0.04% per annum

Minimum
  Denomination:        $1,000



Interest Payment
  Period:              Monthly

Specified Currency:    U.S. Dollars

Issue Price:           99.960%

Settlement Date
  (Original Issue
  Date):               August 30, 1996

Initial Interest Reset
  Date:                September 26, 1996, or if such day is not a Business Day, the next succeeding
                       Business Day, except that if such Business Day is in the next succeeding
                       calendar month, such Initial Interest Reset Date shall be the next preceding
                       day that is a Business Day

Interest Reset Dates:  Same as Interest Payment Dates


Interest Reset Period: Monthly

Interest Determination
  Dates:               Two London Banking Days prior to each Interest Reset Date



Reporting Service:     Telerate (Page 3750)

Book Entry Note or
  Certificated Note:   Book Entry Note

Senior Note or
  Subordinated Note:   Senior Note

Calculation Agent:     The Chase Manhattan Bank



Capitalized terms not defined above have the meanings given to such terms in
the accompanying Prospectus Supplement.


                             MORGAN STANLEY & CO.
                                 Incorporated