GENERAL CALIFORNIA MUNICIPAL MONEY MARKET FUND
497, 1997-05-09
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May 10, 1997
GENERAL CALIFORNIA MUNICIPAL MONEY MARKET FUND
Supplement to Prospectus
Dated December 2, 1996

        EFFECTIVE JUNE 1, 1997, THE FOLLOWING INFORMATION SUPERSEDES ANY
CONTRARY INFORMATION CONTAINED IN THE FUND'S PROSPECTUS.
        The Telephone Redemption Privilege is granted automatically unless
you specifically refuse it by checking the applicable "No" box on the Account
Application. The Telephone Redemption Privilege may be established for an
existing account by a separate signed Shareholder Services Form or by oral
request from any of the authorized signatories on the account by calling
1-800-645-6561.
                                                                573s051097



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