BEAR STEARNS COMPANIES INC
424B3, 1996-10-17
SECURITY BROKERS, DEALERS & FLOTATION COMPANIES
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     PRICING SUPPLEMENT NO. 79                               Rule 424(b)(3)
     DATED: October 16, 1996                             File No. 333-03685
     (To Prospectus dated May 23, 1996
     and Prospectus Supplement dated May 23, 1996)


                               $4,954,795,162
                      THE BEAR STEARNS COMPANIES INC.
                        MEDIUM-TERM NOTES, SERIES B
          WITH MINIMUM MATURITY OF NINE MONTHS FROM DATE OF ISSUE


 Principal Amount:            Floating Rate Notes  Book Entry Notes
 $5,000,000                   [x]                  [x]

 Original Issue Date:         Fixed Rate Notes     Certificated Notes
 10/21/96                     [_]                  [_]

 Maturity Date: 04/21/98

 Option to Extend Maturity:   No  [x]

                              Yes [_]   Final Maturity Date:

                                      Optional           Optional
                    Redemption        Repayment          Repayment
 Redeemable On      Price(s)          Date(s)            Price(s)
 -------------      --------          -------            --------

 N/A                N/A               N/A                N/A

Applicable Only to Fixed Rate Notes:
- -----------------------------------

Interest Rate:  

Applicable Only to Floating Rate Notes:
- --------------------------------------

 Interest Rate Basis:                  Maximum Interest Rate: N/A

 [_]  Commercial Paper Rate            Minimum Interest Rate: N/A

 [_]  Federal Funds Rate               Interest Reset Date(s): *

 [x]  Treasury Rate                    Interest Reset Period: Weekly

 [_]  LIBOR Reuters                    Interest Payment Date(s): **

 [_]  LIBOR Telerate

 [_]  Prime Rate

 [_]  CMT Rate

 Initial Interest Rate: 5.50%          Interest Payment Period: Quarterly

 Index Maturity: Three months

 Spread (plus or minus): +.36%

                         
- -------------------------
*    On Tuesday of each week, or the day following the Treasury auction.

**   On the 21st of each January, April, July, October and at maturity.

The distribution of Notes will conform to the requirements set forth in the
applicable sections of Schedule E to the By-laws of the National
Association of Securities Dealers, Inc.



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