PAINEWEBBER MUNICIPAL MONEY MARKET SERIES
497, 1996-10-15
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                PAINEWEBBER RMA CONNECTICUT MUNICIPAL MONEY FUND
            (A SERIES OF PAINEWEBBER MUNICIPAL MONEY MARKET SERIES)

                 Supplement to Prospectus Dated August 29, 1996
 
     The  board  of  trustees  of  PaineWebber  Municipal  Money  Market  Series
("Trust")   has   approved   a   Plan   of   Reorganization   and    Termination
("Reorganization")   for  submission  to  the  shareholders  of  its  portfolio,
PaineWebber RMA Connecticut Municipal Money Fund ("Fund"), at a special  meeting
to  be held November  25, 1996. If  the proposed Reorganization  is approved and
implemented, all the Fund's assets will be acquired and its liabilities  assumed
by PaineWebber RMA Tax-Free Fund, Inc. ("PW Fund") in a tax-free reorganization.
As  a result of the Reorganization, the  two funds' assets would be combined and
each Fund shareholder would, on the  closing date of the transaction, receive  a
number  of full and fractional shares of PW Fund having an aggregate value equal
to the value of the shareholder's holdings  in the Fund. PW Fund is an  open-end
management  investment company organized as a Maryland corporation. There can be
no assurance that the Fund's shareholders will approve the Reorganization.
 
     The meeting of  Fund shareholders to  consider the proposed  Reorganization
will  be held on  November 25, 1996. If  approved at the  meeting, sales of Fund
shares will cease as of 12:00 noon, Eastern time, on November 25, 1995, so  that
Fund  shares will no longer be available for purchase thereafter. Redemptions of
Fund shares may be effected through the closing of the Reorganization, which  is
scheduled to take place as of 12:00 noon, Eastern time, on November 26, 1996.

Supplement Dated: October 15, 1996



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