BEAR STEARNS COMPANIES INC
424B3, 1996-06-27
SECURITY BROKERS, DEALERS & FLOTATION COMPANIES
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     PRICING SUPPLEMENT NO. 13                               Rule 424(b)(3)
     DATED: June 21, 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
 $13,000,000                  [x]                  [x]

 Original Issue Date:         Fixed Rate Notes     Certificated Notes
 06/28/96                     [_]                  [_]

 Maturity Date: 06/28/01
 
 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: Quarterly

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

 [_]  LIBOR Telerate

 [_]  Prime Rate

 [x]  CMT Rate

 Initial Interest Rate: ***            Interest Payment Period: Quarterly

 Index Maturity:  Two Years

 Spread (plus or minus): + 0.10%
                         
- -------------------------

*    The 28th of each June, September, December and March.

**   The 28th of each June, September, December and March commencing
     09/28/96.

***  The CMT Rate on 06/26/96 plus 10 basis points.

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



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