GENERAL CALIFORNIA MUNICIPAL MONEY MARKET FUND
497, 1994-08-25
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                                                             August 24, 1994
                GENERAL CALIFORNIA MUNICIPAL MONEY MARKET FUND
                SUPPLEMENT TO PROSPECTUS DATED DECEMBER 1, 1993
        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 ("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 (i) borrow money from banks for temporary
or emergency (not leveraging) purposes in an amount up to 15% of the Fund's
total assets, (ii) pledge its assets to the extent necessary to secure
borrowings and make such policy non-fundamental, and (iii) 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
        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.
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 Corporatio
n 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 SUPERSEDES INFORMATION
CONTAINED IN THE SECTION IN THE FUND'S PROSPECTUS ENTITLED "REDEMPTION OF
FUND SHARES -- REDEMPTION BY WIRE OR TELEPHONE" AND DESCRIBES A NEW TELEPHONE
REDEMPTION PRIVILEGE.
        WIRE REDEMPTION PRIVILEGE -- An investor may request by wire or
telephone that redemption proceeds (minimum $1,000) be wired to the
investor's account at a bank which is a member of the Federal Reserve System,
or a correspondent bank if the investor's bank is not a member. An investor
may direct that redemption proceeds be paid by check (maximum $150,000 per
day)made out to the owners of record and mailed to the investor's address.
Redemption proceeds of less than $1,000 will be paid automatically by check.
Holders of jointly registered Fund or bank accounts may have redemption
proceeds of only up to $250,000 wired within any 30-day period. The Fund
reserves the right to refuse any redemption request, including requests made
shortly after a change of address, and may limit the amount involved or the
number of such requests.
        TELEPHONE REDEMPTION PRIVILEGE -- An investor may redeem Fund shares
(maximum $150,000 per day) by telephone if the investor has checked the
appropriate box on the Fund's Account Application or has filed a Shareholder
Services Form with the Transfer Agent. The redemption proceeds will be paid
by check and mailed to the investor's address. An investor may telephone
redemption instructions by calling 1-800-221-4060 or, if the investor is
calling from overseas, call 1-401-455-3306. The Fund reserves the right to
refuse any request made by telephone, including requests made shortly after a
change of address, and may limit the amount involved or the number of
telephone redemption requests. This Privilege may be modified or terminated
at any time by the Transfer Agent or the Fund. Shares for which certificates
have been issued are not eligible for this Privilege.
    573stkr082494



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