PAINEWEBBER MUNICIPAL MONEY MARKET SERIES
24F-2NT, 1997-08-28
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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

===============================================================================
1.    Name and address of issuer:

      PaineWebber Municipal Money Market Series
      1285 Avenue of the Americas
      New York, New York  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
 
- --------------------------------------------------------------------------------
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, 1997

- --------------------------------------------------------------------------------
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:


                                                                 /__/
- --------------------------------------------------------------------------------
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:

      30,339,287 shares representing $30,339,287
- --------------------------------------------------------------------------------

<PAGE>


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

      38,159,263 shares representing $38,159,263

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

      300,368,939 shares representing $300,368,939 (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:

      298,995,176 shares representing $298,995,176
- --------------------------------------------------------------------------------

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):

      1,373,763 shares representing $1,373,763

- --------------------------------------------------------------------------------
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):                  $298,995,176
                                                        --------------------
    (ii)    Aggregate price of shares
            issued in connection with
            dividend reinvestment plans
            (from Item 11, if applicable):   +             1,373,763
                                                        --------------------
   (iii)    Aggregate price of shares
            redeemed or repurchased during
            the fiscal year
            (if applicable):                 -          300,368,939
                                                        --------------------
    (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
                                                        --------------------
- --------------------------------------------------------------------------------

                                       2
<PAGE>


- --------------------------------------------------------------------------------
      (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               1/33 of 1%
                                                       ---------------------
    (vii)   Fee due (line (1) or
            line (v) multiplied by
            line (vi)                                   $     0
                                                       --------------------

- --------------------------------------------------------------------------------
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 & Treasurer
                                   -------------------------------------
Date: August 28, 1997
      ------------------
- --------------------------------------------------------------------------------

================================================================================


                                       3




                            KIRKPATRICK &LOCKHART LLP
                         1800 Massachusetts Avenue, N.W.
                          Washington, D. C. 20036-1800
                            Telephone (202) 778-9000


                                 August 28, 1997


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,  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,  and which were sold during the fiscal  period ended June 30,
1997.

      We  have,  as  counsel,   participated  in  various   business  and  other
proceedings relating to the Trust. We have examined copies,  either certified or
otherwise  proved to be genuine,  of its  Declaration of Trust and By-Laws,  and
other documents  relating to the  organization and operation of the Trust and we
are generally familiar with its business affairs. Based on the foregoing,  it is
our  opinion  that the shares of the Trust sold during the fiscal  period  ended
June 30, 1997, the  registration of which will be made definite by the filing of
the Rule 24f-2 Notice, were legally issued, fully paid and non-assessable.

      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


<PAGE>



PaineWebber Municipal Money Market Series
August 28, 1997
Page 2



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 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

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



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