PRICING SUPPLEMENT NO. 104                              Rule 424(b)(3)
     DATED: November 20, 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
 $10,000,000                  [_]                  [x]

 Original Issue Date:         Fixed Rate Notes     Certificated Notes
 11/22/96                     [x]                  [_]

 Maturity Date: 11/24/97

 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:  5.62%

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): 
                         
- -------------------------

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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