GENERAL CALIFORNIA MUNICIPAL MONEY MARKET FUND
24F-2NT, 1995-09-27
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                 GENERAL CALIFORNIA 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 CALIFORNIA MUNICIPAL MONEY MARKET FUND
      Registration Statement No. 33-9452 - CIK #803951

Gentlemen:

    On November 24, 1986, the Registration Statement of General California
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 July
31, 1995.

    The following information is furnished:


                                                  SHARES        DOLLAR AMOUNT

    (a) Total number of shares sold during
        fiscal year ended 7/31/95 subject
        to registration under Rule 24f-2:  1,802,148,456    $1,802,148,456

    (b) Less shares redeemed during
        fiscal year ended 7/31/95:         2,053,110,924     2,053,110,924
                                          ---------------    ----------------

     Net Sales During Year [(c)-(d)]:       (  250,962,468)   ($  250,962,468)
                                           ================   ================


                              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/ems

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



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