BEAR STEARNS COMPANIES INC
424B3, 1996-07-29
SECURITY BROKERS, DEALERS & FLOTATION COMPANIES
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     PRICING SUPPLEMENT NO.34                                Rule 424(b)(3)
     DATED: July 26, 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
 $50,000,000                  [x]                  [x]

 Original Issue Date:         Fixed Rate Notes     Certificated Notes
 07/29/96                     [_]                  [_]

 Maturity Date: 07/29/97

 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:  

 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): *

 [_]  Treasury Rate                    Interest Reset Period: Monthly

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

 [x]  LIBOR Telerate

 [_]  Prime Rate                       Interest Payment Period: Monthly

 [_]  CMT Rate

 Initial Interest Rate: 5.4875%

 Index Maturity:  One month

 Spread (plus or minus): +0.05%
                         
- -------------------------

  *  The 29th of each month commencing 08/29/96.

 **  The 29th of each month commencing 08/29/96 and 07/29/97.

     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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