GENERAL MUNICIPAL MONEY MARKET FUND INC
497, 1994-08-04
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                                                        August 3, 1994
                           GENERAL MUNICIPAL MONEY
                              MARKET FUND, INC.
                           SUPPLEMENT TO PROSPECTUS
                           DATED FEBRUARY 25, 1994
I.    PROPOSED MERGER OF THE DREYFUS CORPORATION
    The Fund's adviser, The Dreyfus Corporation ("Dreyfus"), has entered
into an Agreement and Plan of Merger (the "Merger Agreement") providing
for the merger (the "Merger") of Dreyfus with a subsidiary of Mellon Bank,
N.A. ("Mellon").
    Following the Merger, it is planned that Dreyfus will be a direct
subsidiary of Mellon. Closing of the Merger is subject to a number of
contingencies, including approvals of the stockholders of Dreyfus and of
Mellon. The Merger is expected to occur in late August 1994, but could
occur significantly later.
    The Merger will result in the automatic termination of the Fund's
current investment advisory agreement with Dreyfus, as required by the
Investment Act of 1940, as amended.
II.    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, to become effective upon
consummation of the Merger, 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.
III.    REVISED MANAGEMENT POLICIES
    THE FOLLOWING INFORMATION SUPPLEMENTS AND SHOULD BE READ IN
CONJUNCTION WITH THE SECTION IN THE FUND'S PROSPECTUS ENTITLED
"DESCRIPTION OF THE FUND -- 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
                      (CONTINUED ON REVERSE SIDE)
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.
IV.    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 Dreyfus Service Corporation for shareholder and
distribution services from The Dreyfus Corporation's assets, including
past profits but not including the management fee paid by the Fund.
Dreyfus Service Corporation 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 OF THE FUND'S PROSPECTUS ENTITLED
"GENERAL INFORMATION."
    With respect to shareholder inquiries made from Long Island, call 794-
5452.
918/stkr080394


                                                  August 3, 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 Dreyfus Service Corporation for shareholder and
distribution services from The Dreyfus Corporation's assets,
including past profits but not including the management fee paid
by the Fund.  Dreyfus Service Corporation 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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