DREYFUS GENERAL NEW YORK MUNICIPAL MONEY MARKET FUND, 497J, 1997-04-01

DREYFUS GENERAL NEW YORK MUNICIPAL MONEY MARKET FUND
497J, 1997-04-01

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                                        April 1, 1997



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

Attention:  Filings - Rule 497(j)

Re:  General New York Municipal Money Market Fund
     Registration Statement File No.: 33-9451
     CIK No. 0000803950

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. 15 to the
Fund's Registration Statement on Form N-1A filed pursuant to Rule 485(b) with
the Securities and Exchange Commission on March 27, 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
     Ernst & Young LLP