GENERAL MONEY MARKET FUND INC
497, 1994-08-25
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                                                             August 24, 1994
                       GENERAL MONEY MARKET FUND, INC.
                  SUPPLEMENT TO PROSPECTUS DATED MARCH 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 this date, the previously announced merger between The Dreyfus
Corporation and a subsidiary of Mellon Bank Corporation ("Mellon") was
completed, and as a result, The Dreyfus Corporation 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.NEW RULE 12B-1 PLAN ARRANGEMENTS IMPLEMENTED
        THE FOLLOWING INFORMATION SUPERSEDES AND REPLACES THE INFORMATION IN
THE FIRST AND THIRD PARAGRAPHS CONTAINED IN THE SECTION IN THE FUND'S
PROSPECTUS ENTITLED "SERVICE PLAN."
        Under the Service Plan, adopted pursuant to Rule 12b-1 under the
Investment Company Act of 1940, the Fund directly bears the costs of
preparing, printing and distributing prospectuses and statements of
additional information and of implementing and operating the Service Plan. In
addition, the Fund reimburses (a) the Distributor for payments made for
distributing the Fund's shares and servicing shareholder accounts
("Servicing") and (b) The Dreyfus Corporation, Dreyfus Service Corporation
and any affiliate of either of them (collectively, "Dreyfus") for payments
made for Servicing, at an aggregate annual rate of up to .20 of 1% of the
value of the Fund's average daily net assets. Each of the Distributor and
Dreyfus may pay one or more Service Agents a fee in
(CONTINUED ON REVERSE SIDE)
respect of the Fund's shares owned by shareholders with whom the Service
Agent has a Servicing relationship or for whom the Service Agent is the
dealer or holder of record. The schedule of such fees and the basis upon
which such fees will be paid shall be determined from time to time by the
Fund's Board. If a Fund shareholder ceases to be a client of a Service Agent,
but continues to hold Fund shares, Dreyfus will be permitted to act as a
Service Agent in respect of such Fund shareholder and receive payments under
the Service Plan from the Distributor for Servicing. The fees payable for
Servicing are payable without regard to actual expenses incurred.
IV.  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 The Dreyfus Corporation, and (ii) a
new Service Plan, each of which became effective upon consummation of the
merger between The Dreyfus Corporation and a subsidiary of Mellon, (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.
V.    REVISED MANAGEMENT POLICIES
        BORROWING MONEY -- As a fundamental policy, the Fund is permitted to
borrow money only 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/stkr082494



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