EXHIBIT 31.1
                                  CERTIFICATION



I, Michael A.J. Farrell, certify that:

1.                I have reviewed this quarterly report on Form 10-Q of Annaly
                  Mortgage Management, Inc. (the "registrant")

2.                Based on my knowledge, this quarterly 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
                  quarterly report;

3.                Based on my knowledge, the financial statements, and other
                  financial information included in this quarterly report,
                  fairly present in all material respects the financial
                  condition, results of operations and cash flows of the
                  registrant as of, and for, the periods presented in this
                  quarterly report;

4.                The registrant's other certifying officer and I am responsible
                  for establishing and maintaining disclosure controls and
                  procedures (as defined in Exchange Act Rules 13a-14 and
                  15d-14) for the registrant and we 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)  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 the end of the period covered by this
               report based on such evaluation; and

          (c)  Disclosed in this report any change in the registrant's internal
               control over financial reporting that occurred during the
               registrant's most recent fiscal quarter 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 and I have
                  disclosed, based on our most recent evaluation of internal
                  control over financial reporting, 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

          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: November 12, 2003
                               /s/ Michael A.J. Farrell
                               ------------------------
                               Michael A.J. Farrell
                               Chairman of the Board of Directors, Chief
                               Executive Officer, President
                               and principal executive officer



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