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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:  March 15, 2006

By: /s/ Bruce R. Bent II
    --------------------
    Name:  Bruce R. Bent II
    Title: Co-Chief Financial Officer


By: /s/ Arthur T. Bent III
    ----------------------
    Name:  Arthur T. Bent III
    Title: Co-Chief Executive Officer


By: /s/ Patrick J. Farrell
    ----------------------
    Name:  Patrick J. Farrell
       Title: Chief 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.