BEAR STEARNS COMPANIES INC
424B3, 1995-06-27
SECURITY BROKERS, DEALERS & FLOTATION COMPANIES
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     PRICING SUPPLEMENT NO. 79                               Rule 424(b)(3)
     DATED:  June 23, 1995                                File No. 33-55673
     (To Prospectus dated October 7, 1994
     and Prospectus Supplement dated October 7, 1994)


                               $3,891,376,750
                      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
 $25,000,000                  [x]                 [x]

 Original Issue Date:         Fixed Rate Notes    Certificated Notes
 06/28/95                     [_]                 [_]

 Maturity Date: 06/28/96

 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: Daily

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

 [_]  Prime Rate

 [_]  CMT Rate

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

 Index Maturity:  N/A

 Spread (plus or minus): +.20%

- -------------------------
*    For the purpose of this Note, "Federal Funds Rate" means, with respect
     to any Interest Determination Date, the Federal Funds Open Rate which
     appears on Telerate Page 5 (or such other page as may replace such
     Telerate Page 5 for the purpose of displaying the Federal Funds Open
     Rate) or, if no such rate is available on the Calculation Date
     pertaining to such Interest Determination Date, the Federal Funds Rate
     will be the rate on such Interest Determination Date as published in
     H.15(519) under the heading "Federal Funds (Effective)."  If neither
     of such rates is published by 3:00 P.M., New York City time, on the
     Calculation Date pertaining to such Interest Determination Date, the
     Federal Funds Rate for such Interest Determination Date will be
     calculated by the Calculation Agent and will be the 

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     arithmetic mean of the rates for the last transaction in overnight
     Federal Funds arranged by three leading brokers of federal funds
     transactions in the City of New York selected by the Calculation Agent
     as of 11:00 A.M., New York City time, on such Interest Determination
     Date; provided, however, that if the brokers selected as aforesaid by
     the Calculation Agent are not quoting as mentioned in this sentence, 
     the rate of interest in effect for the applicable period will be the
     rate of interest in effect on such Interest Determination Date.

**   Daily on each Business Day.

***  09/28/95, 12/28/95, 03/28/96 and 06/28/96.

**** The Federal Funds Rate as of June 27, 1995 plus 20 basis points.

The Interest Determination Date is the Business Day immediately preceding
each Interest Reset Date.

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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