DREYFUS GENERAL NEW YORK MUNICIPAL MONEY MARKET FUND
24F-2NT, 1995-01-27
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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 #803950

Gentlemen:

    On November 24, 1986, the Registration Statement of General New York
Municipal Money Market Fund was declared effective by the SEC.  The Amendment
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, 1994.

    The following information is furnished:

    (a) Shares registered under Securities Act
        of 1933 other than pursuant to Rule 24f(2)
        which remained unsold on 12/1/93:                          None

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

    Post-Effective Amendment No. 10 effective 4/28/94:            29,868,337
                                                              --------------


    Total of (a) and (b)                                          29,868,337
                                                              ==============


                                                  SHARES        DOLLAR AMOUNT

    (c) Total number of shares sold during
        fiscal year ended 11/30/94 subject
        to registration under Rule 24f-2:   1,264,417,457     $1,264,417,457

    (d) Less shares redeemed during
        fiscal year ended 11/30/94:         1,201,510,009      1,201,510,009
                                           --------------     --------------

     Net Sales During Year [(c)-(d)]:          62,907,448     $   62,907,448
                                           ==============     ==============

     Less shares registered other than pur-
     suant to Section 24(f)  ((a) + (b))       29,868,337         29,868,337
                                           --------------     --------------


     Balance                                   33,039,111         33,039,111


                                      -2-


                              CALCULATION OF FEE

    Net sales dollar amount of $33,039,111 at 1/29 of 1% = $11,392.88.

   Funds in the amount of $11,392.88, representing the registration fee, were
wired to CIK #803950.  An opinion of counsel is enclosed.



                                                   Very truly yours,

JJP/ems

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



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