DREYFUS GENERAL NEW YORK MUNICIPAL MONEY MARKET FUND
24F-2NT, 1994-01-27
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                   GENERAL NEW YORK MUNICIPAL MONEY MARKET FUND
                         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 NEW YORK MUNICIPAL MONEY MARKET FUND
      Registration Statement No. 33-9451 - CIK #00000803950

Gentlemen:

    On November 24, 1986, the Registration Statement of General New York
Municipal Money Market Fund 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 November 30, 1993.

    The following information is furnished:

    (a) Shares registered under Securities Act
        of 1933 other than pursuant to Rule 24f(2):                 None



                                                  SHARES        DOLLAR AMOUNT

    (b) Total number of shares sold during
        fiscal year ended 11/30/93 subject
        to registration under Rule 24f-2:   1,221,685,329    $1,221,685,329

    (c) Less shares redeemed during
        fiscal year ended 11/30/93:         1,251,263,666     1,251,263,666
                                           ---------------   ---------------

     Net Sales During Year [(b)-(c)]:       (   29,578,337)   ($   29,578,337)

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


                              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,
MNJ/ems

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


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