GENERAL MONEY MARKET FUND INC
24F-2NT, 1995-03-23
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                        GENERAL 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 MONEY MARKET FUND, INC.
      Registration Statement No. 2-72836 - CIK #00000353560

Gentlemen:

    On November 5, 1981, the Registration Statement of General 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 under Securities Act
        of 1933 other than pursuant to Rule 24f(2)
        which remained unsold on 2/1/94:                        338,495,205

    (b) Shares registered during fiscal year
        other than pursuant to Section 24(f)

        Post-Effective Amendment No. 18 effective 12/8/94:       88,148,217
                                                                 -----------

        Total of (a) and (b)                                    426,643,422
                                                                ===========

                                                 SHARES        DOLLAR AMOUNT

    (c) Total number of shares sold during
        fiscal year ended 1/31/95 subject
        to registration under Rule 24f-2:   3,846,418,471   $3,846,418,471

     (d) Less shares redeemed during
         fiscal year ended 1/31/95:         3,910,940,423    3,910,940,423
                                            -------------    -------------








                                     -2-

      Net Sales During Year [(c)-(d)]:       (  64,521,952)  (  64,521,952)
                                              =============   =============

      Less shares registered other than
      pursuant to Section 24(f) [(a)+(b)]      426,643,422     426,643,422
                                               -----------     ------------

      balance                                 (491,165,374)   ($491,165,374)

      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


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



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