GENERAL MONEY MARKET FUND INC, 497J, 1997-06-10

GENERAL MONEY MARKET FUND INC
497J, 1997-06-10

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                                                 June 10, 1997



Securities and Exchange Commission
Judiciary Plaza
450 Fifth Street, N.W.
Washington, D.C. 20549

Attention:  Filings - Rule 497(j)

Re:  General Money Market Fund, Inc.
     CIK No. 0000353560
     1940 Act File No. 811-3207
     Registration Statement File No. 2-72836

Dear Sir/Madam:

     Pursuant to Rule 497(j) under the Securities Act of 1933, please be
advised that there are no changes to the Prospectus and Statement of
Additional Information contained in Post-Effective Amendment No. 24 to the
Fund's Registration Statement on Form N-1A filed pursuant to Rule 485(b) with
the Securities and Exchange Commission on May 30, 1997.

     Please address any comments or questions to the undersigned at (212) 922-
6785.


                                                           Very truly yours,



                                                           Lawrence T.  Shepps



LTS:kwm
Enclosure

cc:  J. Farragher
     Stroock & Stroock & Lavan LLP
     Ernst & Young LLP