GENERAL MUNICIPAL MONEY MARKET FUND INC
497, 1994-09-27
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                                                         September 26, 1994
                GENERAL MUNICIPAL MONEY MARKET FUND, INC.
            SUPPLEMENT TO PROSPECTUS DATED FEBRUARY 25, 1994
        THE FOLLOWING ANTICIPATED CHANGES HAVE OCCURRED:
I.    CONSUMMATION OF THE MERGER
        THE FOLLOWING INFORMATION SUPPLEMENTS AND SUPERSEDES ANY CONTRARY
INFORMATION CONTAINED IN THE FUND'S PROSPECTUS.
        On August 24, 1994, the previously announced merger between The
Dreyfus Corporation  ("Dreyfus") and a subsidiary of Mellon Bank Corporation
("Mellon") was completed, and as a result, Dreyfus now is a wholly-owned
subsidiary of Mellon Bank, N.A. instead of a publicly-owned corporation.
        Mellon is a publicly owned multibank holding company incorporated
under Pennsylvania law in 1971 and registered under the Federal Bank Holding
Company Act of 1956, as amended. Mellon provides a comprehensive range of
financial products and services in domestic and selected international
markets. Mellon is among the twenty-five largest bank holding companies in
the United States based on total assets. Mellon's principal wholly-owned
subsidiaries are Mellon Bank, N.A., Mellon Bank (DE) National Association,
Mellon Bank (MD), The Boston Company, Inc., AFCO Credit Corporation and a
number of companies known as Mellon Financial Services Corporations. Through
its subsidiaries, Mellon managed more than $130 billion in assets as of July
31, 1994, including approximately $6 billion in mutual fund assets. As of
June 30, 1994, various subsidiaries of Mellon provided non-investment
services, such as custodial or administration services, for approximately
$747 billion in assets, including approximately $97 billion in mutual fund
assets.
II.  NEW DISTRIBUTOR
        THE FOLLOWING INFORMATION SUPERSEDES AND REPLACES ANY CONTRARY
INFORMATION CONTAINED IN THE FUND'S PROSPECTUS AND SPECIFICALLY IN THE
SECTION ENTITLED "HOW TO BUY FUND SHARES."
        The Fund's distributor is Premier Mutual Fund Services, Inc. (the
"Distributor"), located at One Exchange Place, Boston, Massachusetts 02109.
The Distributor is a wholly-owned subsidiary of Institutional Administration
Services, Inc., a provider of mutual fund administration services, the parent

company of which is Boston Institutional Group, Inc.
        Accordingly, references in the Prospectus to Dreyfus Service
Corporation as the Fund's distributor should be substituted with Premier
Mutual Fund Services, Inc.
III.RESULTS OF FUND SHAREHOLDER VOTE
        THE FOLLOWING INFORMATION SUPPLEMENTS AND SUPERSEDES ANY CONTRARY
INFORMATION CONTAINED IN THE FUND'S PROSPECTUS.
        On August 3, 1994, the Fund's shareholders voted to (a) approve a new

investment advisory agreement with Dreyfus, which became effective upon
consummation of the merger between Dreyfus and a subsidiary of Mellon, and
(b) change certain of the Fund's fundamental policies and investment
restrictions to permit the Fund to invest up to 10% of the value of its net
assets in illiquid securities and make such policy non-fundamental.
                        (CONTINUED ON REVERSE SIDE)
IV.  REVISED MANAGEMENT POLICIES
        ILLIQUID SECURITIES -- The Fund may invest up to 10% of the value of
its net assets in securities as to which a liquid trading market does not
exist, provided such investments are consistent with the Fund's investment
objective. Such securities may include securities that are not readily
marketable, such as certain securities that are subject to legal or
contractual restrictions on resale, and repurchase agreements providing for
settlement in more than seven days after notice.  As to these securities, the

Fund is subject to a risk that should the Fund desire to sell them when a
ready buyer is not available at a price the Fund deems representative of
their value, the value of the Fund's net assets could be adversely affected.
V.    OTHER MATTERS
        Effective June 1, 1994, the Fund's Service Plan has been terminated.
The Fund will continue to bear directly the costs of preparing and printing
prospectuses and statements of additional information used for regulatory
purposes and for distribution to existing shareholders. The Dreyfus
Corporation may pay Premier Mutual Fund Services, Inc. for shareholder
services from The Dreyfus Corporation's assets, including past profits but
not including the management fee paid by the Fund. Premier Mutual Fund
Services, Inc. may use part or all of such payments to pay securities dealers
or others in respect of these services.
          THE FOLLOWING INFORMATION RELATING TO SHAREHOLDER INQUIRIES MADE BY

TELEPHONE FROM LONG ISLAND SUPERSEDES THAT CONTAINED IN THE FOURTH PARAGRAPH
OF THE SECTION IN THE FUND'S PROSPECTUS ENTITLED "GENERAL INFORMATION."
          With respect to shareholder inquiries made from Long Island, call
794-5452.
          918/stkr092694

                                             September 26, 1994

            GENERAL MUNICIPAL MONEY MARKET FUND, INC.
      Supplement to the Statement of Additional Information
                     Dated February 25, 1994

     At a meeting of Fund shareholders held on August 3, 1994,
shareholders approved a new Investment Restriction which
supersedes and replaces the Fund's current Investment
Restriction numbered 6 in the section in the Fund's Statement of
Additional Information entitled "Investment Objective and
Management Policies--Investment Restrictions."  Investment
Restriction number 6 is not a fundamental policy and may be
changed by vote of a majority of the Fund's Board members at any
time.  The Fund may not:

     6.  Enter into repurchase agreements providing for
settlement in more than seven days after notice or purchase
securities which are illiquid if, in the aggregate, more than
10% of the value of the Fund's net assets would be so invested.


     The following information supplements and should be read in
conjunction with the section in the Fund's Statement of
Additional Information entitled "Investment Objective and
Management Policies."

     Illiquid Securities.  When purchasing securities that have
not been registered under the Securities Act of 1933, as
amended, and are not readily marketable, the Fund will endeavor
to obtain the right to registration at the expense of the
issuer.  Generally, there will be a lapse of time between the
Fund's decision to sell any such security and the registration
of the security permitting sale.  During any such period, the
price of the securities will be subject to market fluctuations.
However, if a substantial market of qualified institutional
buyers develops pursuant to Rule 144A under the Securities Act
of 1933, as amended, for certain unregistered securities held by
the Fund, the Fund intends to treat such securities as liquid
securities in accordance with procedures approved by the Fund's
Board.  Because it is not possible to predict with assurance how
the market for restricted securities pursuant to Rule 144A will
develop, the Fund's Board has directed the Manager to monitor
carefully the Fund's investments in such securities with
particular regard to trading activity, availability of reliable
price information and other relevant information.  To the extent
that, for a period of time, qualified institutional buyers cease
purchasing restricted securities pursuant to Rule 144A, the
Fund's investing in such securities may have the effect of
increasing the level of illiquidity in the Fund's portfolio
during such period.


     Effective June 1, 1994, the Fund's Service Plan has been
terminated.  The Fund will continue to bear directly the costs
of preparing and printing prospectuses and statements of
additional information used for regulatory purposes and for
distribution to existing shareholders.  The Dreyfus Corporation
may pay Premier Mutual Fund Services, Inc. for shareholder
services from The Dreyfus Corporation's assets, including past
profits but not including the management fee paid by the Fund.
Premier Mutual Fund Services, Inc. may use part or all of such
payments to pay securities dealers or others in respect of these
services.


     The following information supplements and should be read in
conjunction with the section in the Fund's Statement of
Additional Information entitled "Shareholder Services."

     Dividend ACH.  Dividend ACH permits a shareholder to
transfer electronically their dividends or dividends and capital
gains, if any, from the Fund to a designated bank account.  Only
an account maintained at a domestic financial institution which
is an Automated Clearing House member may be so designated.
Banks may charge a fee for this service.  For more information
concerning Dividend ACH, or to request a Dividend Options form,
please call toll free 1-800-645-6561.  You may cancel this
privilege by mailing written notification to The Dreyfus Family
of Funds, P.O. Box 9671, Providence, Rhode Island 02940-9671.
Enrollment or cancellation is effective three business days
following receipt.  This privilege is available only for
existing accounts.  The Fund may modify or terminate this
privilege at any time or charge a service fee.  No such fee is
currently contemplated.






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