GENERAL CALIFORNIA MUNICIPAL MONEY MARKET FUND
24F-2NT, 1996-09-30
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                    U.S. SECURITIES AND EXCHANGE COMMISSION
                            Washington, D.C.  20549

                                   FORM 24F-2
                        Annual Notice of Securities Sold
                            Pursuant to Rule 24f-2

             Read instructions at end of Form before preparing Form.
                             Please print or type.


1.   Name and address of issuer:

       GENERAL CALIFORNIA MUNICIPAL MONEY MARKET FUND
       c/o The Dreyfus Corporation
       200 Park Avenue
       New York, NY  10166

2.   Name of each series or class of funds for which this notice is filed:

       CLASS A and CLASS B

3.   Investment Company Act File Number:  811-4871

     Securities Act File Number:  33-9452

4.   Last day of fiscal year for which this notice is filed:

       July 31, 1996

5.   Check box if this notice is being filed more than 180 days after the
     close of the issuer's fiscal year for purposes of reporting securities
     sold after the close of the fiscal year but before termination of the
     issuer's 24f-2 declaration:
                                                               [   ]

6.   Date of termination of issuer's declaration under rule 24f-2(a)(1),
     if applicable (see Instruction A.6):

                            NOT APPLICABLE

7.   Number of securities of the same class or series which had been
     registered under the Securities Act of 1933 other than pursuant to
     rule 24f-2 in a prior fiscal year, but which remained unsold at the
     beginning of the fiscal year:

                  CLASS A:     None
                  CLASS B:     None

8.   Number of securities registered during the fiscal year other than
     pursuant to rule 24f-2:

                 CLASS A:      251,252,468
                 CLASS B:      None

9.   Number and aggregate sale price of securities sold during the fiscal
     year:

     CLASS A:   Number: 1,404,863,326      Sale Price: $1,404,863,326
     CLASS B:   Number:     5,489,381      Sale Price: $    5,489,381

10.  Number and aggregate sale price of securities sold during the fiscal
     year in reliance upon registration pursuant to rule 24f-2:

     CLASS A:   Number: 1,404,863,326      Sale Price: $1,404,863,326
     CLASS B:   Number:     5,489,381      Sale Price: $    5,489,381

11.  Number and aggregate sale price of securities issued during the fiscal
     year in connection with dividend reinvestment plans, if applicable
     (see Instruction B.7):

     CLASS A:   Number: N/A                Sale Price: N/A
     CLASS B:   Number: N/A                Sale Price: N/A

12.  Calculation of registration fee:

     CLASS A:

   (i)    Aggregate sale price of securities sold during
          the fiscal year in reliance on rule 24f-2
          (from Item 10):                                     $1,404,863,326
                                                             ----------------

   (ii)   Aggregate price of shares issued in connection
          with dividend reinvestment plans (from Item 11,
          if applicable):                                    +    N/A
                                                             ----------------
   (iii)  Aggregate price of shares redeemed or repur-
          chased during the fiscal year (if applicable):     - 1,478,086,875
                                                             ----------------
   (iv)   Aggregate price of shares redeemed or repur-
          chased and previously applied as a reduction
          to filing fees pursuant to rule 24e-2 (if
          applicable):                                       +    N/A
                                                             ----------------
   (v)    Net aggregate price of securities sold and
          issued during the fiscal year in reliance
          on rule 24f-2 [line (i), plus line (ii),
          less line (iii), plus line (iv)] (if appli-
          cable):                                             $  - 0 -
                                                             ----------------

   (vi)   Multiplier prescribed by Section 6(b) of
          the Securities Act of 1933 or other appli-
          cable law or regulation (see Instruction C.6):     x  1/2900
                                                             ----------------

   (vii)  Fee due [line (i) or line (v) multiplied by
          line (vi)]:                                         $ - 0 -
                                                             ================


      CLASS B:

   (i)    Aggregate sale price of securities sold during
          the fiscal year in reliance on rule 24f-2
          (from Item 10):                                      $5,489,381
                                                              --------------

   (ii)   Aggregate price of shares issued in connection
          with dividend reinvestment plans (from Item 11,
          if applicable):                                     +    N/A
                                                              --------------
   (iii)  Aggregate price of shares redeemed or repur-
          chased during the fiscal year (if applicable):      -    14,611
                                                              --------------
   (iv)   Aggregate price of shares redeemed or repur-
          chased and previously applied as a reduction
          to filing fees pursuant to rule 24e-2 (if
          applicable):                                        +    N/A
                                                              --------------
   (v)    Net aggregate price of securities sold and
          issued during the fiscal year in reliance
          on rule 24f-2 [line (i), plus line (ii),
          less line (iii), plus line (iv)] (if appli-
          cable):                                              $5,474,770
                                                              --------------

   (vi)   Multiplier prescribed by Section 6(b) of
          the Securities Act of 1933 or other appli-
          cable law or regulation (see Instruction C.6):      x  1/2900
                                                              --------------

   (vii)  Fee due [line (i) or line (v) multiplied by
          line (vi)]:                                          $1,887.85
                                                              ==============

          TOTAL FEE DUE FOR CLASS A AND CLASS B:               $1,887.85
                                                              ==============



Instruction:  Issuers should complete lines (ii), (iii), (iv), and (v) only
              if the form is being filed within 60 days after the close of
              the issuer's fiscal year.  See Instruction C.3.

13.  Check box if fees are being remitted to the Commission's lockbox depo-
     sitory as described in section 3a of the Commission's Rules of Informal
     and Other Procedures (17 CFR 202.3a).

                                                                   [ X ]

     Date of mailing or wire transfer of filing fees to the Commission's
     lockbox depository:
                         On or about September 27, 1996

                                    SIGNATURES


     This report has been signed below by the following person on behalf of
     the issuer and in the capacity and on the date indicated.



     By (Signature and Title)*
                               /s/ Richard W. Ingram
                               Richard W. Ingram, Vice President


     Date: September 30, 1996


* Please print the name and title of the signing officer below the signature.


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