DREYFUS GENERAL NEW YORK MUNICIPAL MONEY MARKET FUND
497, 1999-04-30
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                                                                    May 1, 1999

                        GENERAL CALIFORNIA MUNICIPAL
                           MONEY MARKET FUND

                            GENERAL MUNICIPAL MONEY
                               MARKET FUND

                          GENERAL NEW YORK MUNICIPAL
                             MONEY MARKET FUND

                           SUPPLEMENT TO PROSPECTUS
                              DATED APRIL 1, 1999

      THE   FOLLOWING   INFORMATION  SUPPLEMENTS  AND  SUPERSEDES  ANY  CONTRARY
INFORMATION  RELATING  TO  THE  FUND  CONTAINED  IN  THE  SECTION  OF THE FUND'S
PROSPECTUS ENTITLED "ACCOUNT POLICIES - BUYING SHARES":

      Your  price  for fund shares is the fund's net asset value (NAV), which is
generally  calculated  three times a day, at 12:00 noon, 2:00 p.m. and 8:00 p.m.
Eastern  time for the municipal money market funds, every day the New York Stock
Exchange  or the fund's transfer agent is open. Your order will be priced at the
next NAV calculated after your order is accepted by the fund's transfer agent or
other authorized entity.

      If  your  payments are received in or converted into Federal Funds by 4:00
p.m.  for  the  municipal  money  market  funds,  you  will receive the dividend
declared  that  day.  If your payments are received in or converted into Federal
Funds  after  4:00 p.m.  you  will  begin to accrue dividends on the following
business day. Qualified institutions may telephone orders to buy shares. If such
an  order is made by 2:00 p.m. for the municipal money market funds, and Federal
Funds  are  received  by  4 p.m.,  the shares will be purchased at the next NAV
determined  after  the telephone order is accepted and will receive the dividend
declared  that  day.  If such an order is made after 2:00 p.m. but by 8:00 p.m.,
and Federal Funds are received by 11 a.m. the next business day, the shares will
be  purchased at the NAV determined at 8 p.m. and will begin to accrue dividends
on the next business day. All times are Eastern time.

                                                                   gens0599/cmn





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