PAINEWEBBER MUNICIPAL MONEY MARKET SERIES
24F-2NT, 1996-08-27
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                       U.S. SECURITIES AND EXCHANGE COMMISSION
                                Washington, D.C. 20549

                                     FORM 24F-2
                           Annual Notice of Securities Sold
                                Pursuant to Rule 24f-2
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       <S>    <C>
       1.       Name and address of issuer:

                PaineWebber Municipal Money Market Series
                1285 Avenue of the Americas
                New York, NY 10019


       2.       Name of each series or class of funds for which this notice is filed:

                PaineWebber RMA Connecticut Municipal Money Fund
                PaineWebber RMA New Jersey Municipal Money Fund
                New York Series


       3.       Investment Company Act File Number:

                811-6173

                Securities Act File Number:

                33-36766

       4.       Last day of fiscal year for which this notice is filed:

                June 30, 1996


       5.       Check box if this notice is being filed more than 180 days after the close of the issuer's fiscal
                year for purposes of reporting securities sold after the close of the fiscal year but before
                termination of the issuer's 24f-2 declaration:

                                                                                                             /_/







     \\DCBDC\DOCS_FILES-58133.02
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       6.       Date of termination of issuer's declaration rule 24f-2(a)(1), if applicable (see Instruction
                A.6):




       7.       Number and amount of securities of the same class or series which had been registered under the
                Securities Act of 1933 other than pursuant to rule 24f-2 in a prior fiscal year, but which
                remained unsold at the beginning of the fiscal year:

                8,427,572 shares representing $8,427,572


       8.       Number and amount of securities registered during the fiscal year other than pursuant to rule
                24f-2:

                21,911,715 shares representing $21,911,715

       9.       Number and aggregate sale price of securities sold during the fiscal year:

                238,925,095 shares representing $237,925,095 (including shares issued in connection with dividend
                reinvestment plans)


       10.      Number and aggregate sale price of securities sold during the fiscal year in reliance upon
                registration pursuant to rule 24f-2:

                237,856,902 shares representing $237,856,902


       11.      Number and aggregate sale price of securities issued during the fiscal year in connection with
                dividend reinvestment plans, if applicable (see Instruction B.7):

                1,068,193 shares representing $1,068,193



















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       12.      Calculation of registration fee:

                (i)     Aggregate sale price of
                        securities sold during the
                        fiscal year in reliance on
                        rule 24f-2 (from Item 10):     $     237,856,902
                                                        --------------------
               (ii)     Aggregate price of shares
                        issued in connection with
                        dividend reinvestment plans
                        (from Item 11, if applicable): +       1,068,193
                                                        --------------------

              (iii)     Aggregate price of shares
                        redeemed or repurchased during
                        the fiscal year
                        (if applicable):                -     238,925,095
                                                        --------------------

               (iv)     Aggregate price of shares
                        redeemed or repurchased and
                        previously applied as a
                        reduction to filing fees
                        pursuant to rule 24e-2
                        (if applicable):                +               0
                                                        --------------------

                (v)     Net aggregate price of
                        securities sold and issued
                        during the fiscal year in
                        reliance on rule 24f-2
                        [line (i), plus line (ii),
                        less line (iii), plus line
                        (iv)] (if applicable):          $               0
                                                        --------------------

               (vi)     Multiplier prescribed by
                        Section 6(b) of the
                        Securities Act of 1933 or
                        other applicable law or
                        regulation (see Instruction
                        C.6):                           x      1/29 of 1%
                                                        -------------------

              (vii)     Fee due (line (1) or
                        line (v) multiplied by
                        line (vi)                       $               0
                                                        -------------------





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       13.      Check box if fees are being remitted to the Commission's lockbox depository as described in
                section 3a of the Commission's Rules of Informal and Other Procedures (17 CFR 202.3a).
                                                                                                     /_/

                Date of mailing or wire transfer of filing fees to the Commission's lockbox depository:



                                                       SIGNATURES

       This report has been signed below by the following persons on behalf of the issuer and in the capacities
       and on the dates indicated.

       By (Signature and Title)  /s/ Paul H. Schubert
                                 -------------------------------------
                                 Paul H. Schubert
                                 -------------------------------------
                                Vice President & Asst Treasurer
                                 -------------------------------------

       Date     August 27, 1996
                ------------------------

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                             Kirkpatrick & Lockhart LLP 
                           1800 Massachusetts Avenue, N.W.
                                Washington, D.C. 20036



                                   August 27, 1996


     PaineWebber Municipal Money Market Series
     1285 Avenue of the Americas
     New York, New York  10019

     Dear Sir or Madam:

              PaineWebber Municipal Money Market Series ("Trust") is an
     unincorporated voluntary association organized under the laws of the
     Commonwealth of Massachusetts pursuant to an Agreement and Declaration of
     Trust dated September 14, 1990, as amended.  We understand that the Trust
     is about to file a Rule 24f-2 Notice pursuant to Rule 24f-2 under the
     Investment Company Act of 1940, as amended ("1940 Act"), for the purpose
     of making definite the number of shares of beneficial interest which it
     has registered thereunder and under the Securities Act of 1933, as amended
     ("1933 Act"), and which were sold during the fiscal period ended June 30,
     1996.

              We have, as counsel to the Trust, been advised of the various
     business and other proceedings relating to the Trust.  We have examined
     copies, either certified or otherwise proved to be genuine, of the
     Declaration of Trust and By-Laws of the Trust and other documents relating
     to its organization and operations.  Based on the foregoing, it is our
     opinion that the shares of the Trust sold during the fiscal period ended
     June 30, 1996, the registration of which will be made definite by the
     filing of the Rule 24f-2 Notice, were legally issued, fully paid and
     nonassessable.  

              The Trust is an entity of the type commonly known as a
     "Massachusetts business trust."  Under Massachusetts law, shareholders
     could, under certain circumstances, be held personally liable for the
     obligations of the Trust.  The Declaration of Trust states that persons
     with claims against the Trust shall look solely to the Trust property for
     satisfaction of claims of any nature arising in connection with the
     affairs of the Trust and that no shareholder shall be subject to any
     personal liability in connection with any liability of the Trust.  It also
     states that notice of such disclaimer may be given in any obligation,
     contract, instrument, certificate, or undertaking made or issued by the
     trustees of the Trust on behalf of the Trust.  The Declaration of Trust
     further provides: (i)  that the Trust shall indemnify and hold each
     shareholder harmless from and against all claims and liabilities to which
     such shareholder may become subject by reason of his being or having been
     a shareholder and (ii) that the Trust shall reimburse such shareholder for
     all legal and other expenses reasonably incurred by the shareholder in
     connection with any such claim or liability, such indemnification and
     reimbursement to be made out of the assets of the one or more series of
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     PaineWebber Municipal Money Market Series
     August 27, 1996
     Page 2

     which the shareholder was a shareholder at the time the act or event
     occurred which gave rise to the claim against or liability of such
     shareholder.  Thus, the risk of a shareholder incurring financial loss on
     account of shareholder liability is limited to circumstances in which the
     Trust or a series thereof would be unable to meet its obligations.

              We hereby consent to this opinion accompanying the Rule 24f-2
     Notice which you are about to file with the Securities and Exchange
     Commission.

                                       Very truly yours,

                                       KIRKPATRICK & LOCKHART LLP

                                          /s/ Elinor W. Gammon
                                       By:------------------------
                                              Elinor W. Gammon
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