PRICING SUPPLEMENT NO. 19                               Rule 424(b)(3)
DATED:  September 12, 1995                           File No. 33-60065
(To Prospectus dated July 28, 1995
and Prospectus Supplement dated July 28, 1995)


                               $2,399,571,350
                      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
 09/14/95                     [_]                 [_]

 Maturity Date: 09/17/96

 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: Monthly

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

 [_]  Prime Rate                      Interest Payment Period: Monthly

 [_]  CMT Rate


 Initial Interest Rate: 5.925%

 Index Maturity:  One Month

 Spread (plus or minus):  +.05%
                         
-------------------------
*   For purposes of this Note, LIBOR will be determined by the Calculation
    Agent in accordance with the following provisions:

    (i) With respect to an Interest Determination Date, LIBOR will be
determined on the basis of the offered rate for deposits in U.S. dollars
having the Index Maturity specified above, commencing on the second London
Banking Day immediately following such Interest Determination Date, which







appears on Telerate page 3750 (or such other page as may replace such
Telerate page 3750 for the purpose of displaying London interbank rates of
major banks), as of 11:00 A.M., London time, on such Interest Determination
Date.  If no such rate appears on Telerate page 3750 (or such other page),
LIBOR for such Interest Determination Date will be determined as if the
parties had specified the rate described in (ii) below.

    (ii) With respect to an Interest Determination Date on which no
offered rate appears on Telerate page 3750 (or such other page) as
described in (i) above, LIBOR will be determined on the basis of the rates
at approximately 11:00 A.M., London time, on such Interest Determination
Date at which deposits in U.S. dollars having the Index Maturity specified
above are offered to prime banks in the London interbank market by four
major banks in the London interbank market selected by the Calculation
Agent commencing on the second London Banking Day immediately following
such Interest Determination Date and in a principal amount equal to an
amount of not less than $1,000,000 that is representative of a single
transaction in such market at such time.  The Calculation Agent will
request the principal London office of each of such banks to provide a
quotation of its rate.  If at least two such quotations are provided, LIBOR
for such Interest Determination Date will be the arithmetic mean of such
quotations.  If fewer than two quotations are provided, LIBOR for such
Interest Determination Date will be the arithmetic mean of the rates quoted
at approximately 11:00 A.M., New York City time, on such Interest
Determination Date by three major banks in the City of New York, selected
by the Calculation Agent for loans in U.S. dollars to leading European
banks, having the specified Index Maturity commencing on the second London
Banking Day immediately following such Interest Determination Date and in a
principal amount equal to an amount of not less than $1,000,000 that is
representative of a single transaction in such market at such time;
provided, however, that if the banks selected as aforesaid by the
Calculation Agent are not quoting as mentioned in this sentence, LIBOR will
be LIBOR in effect on such Interest Determination Date.

**  10/04/95, 11/03/95, 12/05/95, 01/04/96, 02/05/96, 03/05/96, 04/03/96,
    05/03/96, 06/05/96, 07/03/96, 08/05/96 and 09/05/96.

*** 10/04/95, 11/03/95, 12/05/95, 01/04/96, 02/05/96, 03/05/96, 04/03/96,
    05/03/96, 06/05/96, 07/03/96, 08/05/96, 09/05/96 and 09/17/96.

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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