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                                                                 Exhibit 99.CERT

                                 CERTIFICATIONS

I, Bruce R. Bent, certify that:

1.        I have reviewed this report on Form N-CSR of Reserve Municipal Money
Market Trust;

2.        Based on my knowledge, this report does not contain any untrue
statement of a material fact or omit to state a material fact necessary to make
the statements made, in light of the circumstances under which such statements
were made, not misleading with respect to the period covered by this report;

3.        Based on my knowledge, the financial statements, and other financial
information included in this report, fairly present in all material respects the
financial condition, results of operations, changes in net assets, and cash
flows (if the financial statements are required to include a statement of cash
flows) of the registrant as of, and for, the periods presented in this report;

4.        The registrant's other certifying officer(s) and I are responsible for
establishing and maintaining disclosure controls and procedures (as defined in
Rule 30a-3(c) under the Investment Company Act of 1940) for the registrant and
have:

          (a)     Designed such disclosure controls and procedures, or caused
such disclosure controls and procedures to be designed under our supervision, to
ensure that material information relating to the registrant, including its
consolidated subsidiaries, is made known to us by others within those entities,
particularly during the period in which this report is being prepared;

          (b)     [Reserved];

          (c)     Evaluated the effectiveness of the registrant's disclosure
controls and procedures and presented in this report our conclusions about the
effectiveness of the disclosure controls and procedures, as of a date within 90
days prior to the filing date of this report based on such evaluation; and

          (d)     Disclosed in this report any change in the registrant's
internal control over financial reporting that occurred during the second fiscal
quarter of the period covered by this report that has materially affected, or is
reasonably likely to materially affect, the registrant's internal control over
financial reporting; and

5.        The registrant's other certifying officer(s) and I have disclosed to
the registrant's auditors and the audit committee of the registrant's board of
directors (or persons performing the equivalent functions):

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          (a)     All significant deficiencies and material weaknesses in the
design or operation of internal control over financial reporting which are
reasonably likely to adversely affect the registrant's ability to record,
process, summarize, and report financial information; and

          (b)     Any fraud, whether or not material, that involves management
or other employees who have a significant role in the registrant's internal
control over financial reporting.

Date: April 20, 2005

                                                        /s/ Bruce R. Bent
                                                        -----------------
                                                        Bruce R. Bent
                                                        Chairman and CEO

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                                 CERTIFICATIONS

I, Arthur T. Bent III, certify that:

1.        I have reviewed this report on Form N-CSR of Reserve Municipal Money
Market Trust;

2.        Based on my knowledge, this report does not contain any untrue
statement of a material fact or omit to state a material fact necessary to make
the statements made, in light of the circumstances under which such statements
were made, not misleading with respect to the period covered by this report;

3.        Based on my knowledge, the financial statements, and other financial
information included in this report, fairly present in all material respects the
financial condition, results of operations, changes in net assets, and cash
flows (if the financial statements are required to include a statement of cash
flows) of the registrant as of, and for, the periods presented in this report;

4.        The registrant's other certifying officer(s) and I are responsible for
establishing and maintaining disclosure controls and procedures (as defined in
Rule 30a-3(c) under the Investment Company Act of 1940) for the registrant and
have:

          (a)     Designed such disclosure controls and procedures, or caused
such disclosure controls and procedures to be designed under our supervision, to
ensure that material information relating to the registrant, including its
consolidated subsidiaries, is made known to us by others within those entities,
particularly during the period in which this report is being prepared;

          (b)     [Reserved];

          (c)     Evaluated the effectiveness of the registrant's disclosure
controls and procedures and presented in this report our conclusions about the
effectiveness of the disclosure controls and procedures, as of a date within 90
days prior to the filing date of this report based on such evaluation; and

          (d)     Disclosed in this report any change in the registrant's
internal control over financial reporting that occurred during the second fiscal
quarter of the period covered by this report that has materially affected, or is
reasonably likely to materially affect, the registrant's internal control over
financial reporting.

5.        The registrant's other certifying officer(s) and I have disclosed to
the registrant's auditors and the audit committee of the registrant's board of
directors (or persons performing the equivalent functions):

          (a)     All significant deficiencies and material weaknesses in the
design or operation of internal control over financial reporting which are
reasonably likely to adversely affect the registrant's ability to record,
process, summarize, and report financial information; and

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          (b)     Any fraud, whether or not material, that involves management
or other employees who have a significant role in the registrant's internal
control over financial reporting.

Date: April 20, 2005


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