DREYFUS GENERAL NEW YORK MUNICIPAL MONEY MARKET FUND, 497J, 1996-04-17

DREYFUS GENERAL NEW YORK MUNICIPAL MONEY MARKET FUND
497J, 1996-04-17

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                                             April 17, 1996


Filing Desk
Securities and Exchange Commission
Judiciary Plaza
450 Fifth Street, N.W.
Washington, DC 20549

Re:  General New York Municipal Money Market Fund
     1933 Act File No. 33-9451
     1940 Act File No. 811-4870
     CIK No. 0000803950

Dear Sir/Madam:

     Pursuant to Rule 497(j) under the Securities Act of 1933, this is to
certify that the form of Prospectus and Statement of Additional Information
that would have been filed under paragraphs (b) or (c) of this section does
not differ from that contained in the most recent amendment to the Fund's
Registration Statement, electronically filed  with the Securities and
Exchange Commission on March 29, 1996.


                                             Very truly yours,


                                             James Noone
JGN

cc:  Ernst & Young LLP
     Stroock & Stroock & Lavan