GENERAL GOVERNMENT SECURITIES MONEY MARKET FUND INC
24F-2NT, 1995-03-23
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               GENERAL GOVERNMENT SECURITIES MONEY MARKET FUND, INC.
                         c/o THE DREYFUS CORPORATION
                                200 PARK AVENUE
                              NEW YORK, NY  10166




Securities and Exchange Commission
Judiciary Plaza
450 Fifth Street, NW
Washington, DC  20549



    24f-2 Notice - GENERAL GOVERNMENT SECURITIES MONEY MARKET FUND, INC.
    Registration Statement No. 2-77207 - CIK #00000702172

Gentlemen:

    On November 29, 1982, the Registration Statement of General Government
Securities Money Market Fund, Inc. was declared effective by the SEC.  The
Registration Statement represented the Fund's election to register an
indefinite number of shares and this Notice, filed pursuant to Rule 24f-2, is
for the fiscal year ended January 31, 1995.

    The following information is furnished:

    (a) Shares registered during fiscal year
        other than pursuant to Rule 24f(2):

        Post-Effective Amendment No. 17 effective
        12/8/94                                               204,778,321
                                                              ============


                                                  SHARES        DOLLAR AMOUNT

    (b) Total number of shares sold during
        fiscal year ended 1/31/95 subject
        to registration under Rule 24f-2:   4,356,251,849   $4,356,251,849

    (c) Less shares redeemed during
        fiscal year ended 1/31/95:          4,399,218,939    4,399,218,939
                                           ---------------  ---------------

     Net Sales During Year [(b)-(c)]:        (   42,967,090)  ($   42,967,090)

                                            ================  ================

     Less shares registered other than
     pursuant to Section 24(f), and
     the dollar amount thereof [(a) above]:      204,778,321      204,778,321
                                            ---------------     ------------

     Balance:                                 (  247,745,411)   ($247,745,411)

                                            =================   ==============

                                           -2-


                        CALCULATION OF FEE

    Since the shares redeemed exceed the shares sold, no registration fee is
required.  An opinion of counsel is enclosed.


                                                 Very truly yours,




JJP/rtj
                                                 John J. Pyburn,
                                                 Assistant Treasurer

cc:  Mr. J. deMichaelis, SEC
     Ms. R. McLaughlin, E&Y
     Mr. S. Rosenberg, BONY


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