BEAR STEARNS COMPANIES INC
424B3, 1996-10-21
SECURITY BROKERS, DEALERS & FLOTATION COMPANIES
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     PRICING SUPPLEMENT NO. 81                               Rule 424(b)(3)
     DATED: October 18, 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
 $20,000,000                  [_]                 [x]

 Original Issue Date:         Fixed Rate Notes    Certificated Notes
 11/04/96                     [x]                 [_]

 Maturity Date: 11/04/2011

 Option to Extend Maturity:   No  [x]

                              Yes [_]   Final Maturity Date:

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

 *                  100%              N/A                N/A

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

Interest Rate:  8.00%

Interest Payment Dates:  **

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

 Interest Rate Basis:                  Maximum Interest Rate: 

 [_]  Commercial Paper Rate            Minimum Interest Rate: 

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

 [_]  Treasury Rate                    Interest Reset Period: 

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

 [_]  LIBOR Telerate

 [_]  Prime Rate

 [_]  CMT Rate

 Initial Interest Rate:                Interest Payment Period: 
 
 Index Maturity:  

 Spread (plus or minus): 
                         
- -------------------------
*    Commencing November 4, 1997 and on the 4th of May and November in each
     year thereafter, the Notes may be called at 100% of the principal
     amount, in whole but not in part, at the option of the Company on five
     days' notice. 

**   The 4th of May and November in each year, commencing 05/04/97.

The Notes will be issued at prevailing market rates.

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.

 NYFS04...:\25\22625\0122\1773\FFF0096V.11A



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