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                                                              Exhibit 99.906CERT

     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 Reserve Municipal Money
Market Trust (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: February 3, 2005

By:  /s/ Bruce R. Bent
     ------------------
     Name:  Bruce R. Bent
     Title: Chairman and CEO


Dated: February 3, 2005

By:  /s/ Arthur T. Bent III
     ----------------------
     Name: Arthur T. Bent III
     Treasurer (Principal Financial Officer)

        A signed original of this written statement required by Section 906, or
other document authenticating, acknowledging, or otherwise adopting the
signature that appears in typed form within the electronic version of this
written statement required by Section 906, has been provided to the Registrant
and will be retained by the Registrant and furnished to the Securities and
Exchange Commission or its staff upon request.

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