DREYFUS GENERAL NEW YORK MUNICIPAL MONEY MARKET FUND
497, 1995-12-01
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                                             December 1, 1995

          GENERAL NEW YORK MUNICIPAL MONEY MARKET FUND

       Supplement to Statement of Additional Information
                     Dated September 8, 1995

     The following information supplements and supersedes any
contrary information contained in the Fund's Statement of
Additional Information:

     Effective December 1, 1995, Dreyfus Transfer, Inc. (the
"Transfer Agent") became the Fund's transfer and dividend
disbursing agent.  The Transfer Agent, a wholly-owned subsidiary
of the Manager, is located at One American Express Plaza,
Providence, Rhode Island 02903.  Under a transfer agency
agreement with the Fund, the Transfer Agent arranges for the
maintenance of shareholder account records for the Fund, the
handling of certain communications between shareholders and the
Fund and the payment of dividends and distributions payable by
the Fund.  For these services, the Transfer Agent receives a
monthly fee computed on the basis of the number of shareholder
accounts it maintains for the Fund during the month, and is
reimbursed for certain out-of-pocket expenses.  The Transfer
Agent has no part in determining the investment policies of the
Fund or which securities are to be purchased or sold by the Fund.

     How to Buy Fund Shares -- TeleTransfer Privilege.
TeleTransfer purchase orders may be made at any time.  Purchase
orders received by 4:00 P.M., New York time, on any business day
that the Fund's Transfer Agent and the New York Stock Exchange
are open for business will be credited to the shareholder's Fund
account on the next bank business day following such purchase
order.  Purchase orders made after 4:00 P.M., New York time, on
any business day the Transfer Agent and the New York Stock
Exchange are open for business, or orders made on Saturday,
Sunday or any Fund holiday (e.g., when the New York Stock
Exchange is not open for business), will be credited to the
shareholder's Fund account on the second bank business day
following such purchase order.
 

                                                            December 1, 1995
                       GENERAL NEW YORK MUNICIPAL
                           MONEY MARKET FUND
                       SUPPLEMENT TO PROSPECTUS
                       DATED SEPTEMBER 8, 1995
        THE FOLLOWING INFORMATION SUPPLEMENTS OR REPLACES THE INFORMATION
CONTAINED IN THE SECTIONS OF THE FUND'S PROSPECTUS ENTITLED "MANAGEMENT OF
THE FUND," "HOW TO BUY FUND SHARES," "SHAREHOLDER SERVICES," AND "HOW TO
REDEEM FUND SHARES":
        Dreyfus Transfer, Inc., a wholly-owned subsidiary of The Dreyfus
Corporation, is located at One American Express Plaza, Providence, Rhode
Island 02903, and serves as the Fund's Transfer and Dividend Disbursing Agent
(the "Transfer Agent").
        Effective January 1, 1996, the telephone number for the following
transactions is 1-800-645-6561 or, if you are calling from overseas,
516-794-5452:
        *      TELETRANSFER Privilege
        *      Telephone Exchange Privilege
        *      Wire Redemption Privilege
        *      Telephone Redemption Privilege
574s120195
 



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