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                                                         Exhibit EX-99.906.CERT

     Certification Pursuant to Section 906 of the Sarbanes-Oxley Act of 2002
    (Subsections (a) and (b) of Section 1350, Chapter 63 of Title 18, United
                                  States Code)

In connection with the attached report of UBS Municipal Money Market Series (the
"Registrant") on Form N-CSR (the "Report"), each of the undersigned officers of
the Registrant does hereby certify that, to the best of such officer's
knowledge:

     1)   the Report fully complies with the requirements of Section 13(a) or
          15(d), as applicable, of the Securities Exchange Act of 1934, as
          amended;

     2)   the information contained in the Report fairly presents, in all
          material respects, the financial condition and results of operations
          of the Registrant as of, and for, the periods presented in the Report.


Dated: September 7, 2004
       -----------------

By:    /s/ Joseph A. Varnas
       --------------------
       Joseph A. Varnas
       President


Dated: September 7, 2004
       -----------------

By:    /s/ Thomas Disbrow
       ------------------
       Thomas Disbrow
       Treasurer


This certification is being furnished solely pursuant to 18 U.S.C. Section 1350
and is not being filed as part of the Report or as a separate disclosure
document.