GENERAL MONEY MARKET FUND INC
497, 1994-08-04
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                                                   August 3, 1994
                       GENERAL MONEY MARKET FUND, INC.
                           SUPPLEMENT TO PROSPECTUS
                           DATED MARCH 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 Company Act of 1940, as amended. The Merger also will
necessitate implementation of a new Service Plan.
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 (i) a
new investment advisory agreement with Dreyfus, and (ii) a new Service
Plan, each to become effective upon consummation of the Merger, (b) adopt
an amendment to the Fund's Charter to permit the issuance of additional
classes of shares, and (c) change certain of the Fund's fundamental
policies and investment restrictions to permit the Fund to (i) borrow
money from banks for temporary or emergency (not leveraging) purposes in
an amount up to 15% of the value of the Fund's total assets, and (ii) invest
up to 10% of the value of its net assets in illiquid securities and make
such policy non-fundamental.
                   (CONTINUED ON REVERSE SIDE)
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."
    BORROWING MONEY -- As a fundamental policy, the Fund is permitted to
borrow money only from banks for temporary or emergency (not
leveraging) purposes, in an amount up to 15% of the value of the Fund's
total assets (including the amount borrowed) valued at the lesser of cost
or market, less liabilities (not including the amount borrowed) at the time
the borrowing is made. While borrowings exceed 5% of the Fund's total
assets, the Fund will not make any additional investments.
    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.
196/stkr080394


                                                  August 3, 1994


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

     At a meeting of Fund shareholders held on August 3, 1994,
shareholders approved new Investment Restrictions which
supersede and replace the Fund's current Investment Restrictions
numbered 2 and 6 in the section in the Fund's Statement of
Additional Information entitled "Investment Objective and
Management Policies--Investment Restrictions."  Investment
Restriction number 2 is a fundamental policy that cannot be
changed without approval by the holders of a majority (as
defined in the Investment Company Act of 1940, as amended (the
"Act")) of the Fund's outstanding voting shares.  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:

     2.  Borrow money, except from banks for temporary or
emergency (not leveraging) purposes in an amount up to 15% of
the value of the Fund's total assets (including the amount
borrowed) based on the lesser of cost or market, less
liabilities (not including the amount borrowed) at the time the
borrowing is made.  While borrowings exceed 5% of the value of
the Fund's total assets, the Fund will not make any additional
investments.

     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.


     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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