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                                                                    Exhibit 31.1

                                  CERTIFICATION

I, Nassib G. Chamoun, certify that:

   1. I have reviewed this Quarterly Report on Form 10-Q of Aspect Medical
      Systems, Inc.;

   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 and cash flows of
      the registrant as of, and for, the periods presented in this report;

   4. The registrant's other certifying officer and I are responsible for
      establishing and maintaining disclosure controls and procedures (as
      defined in Exchange Act Rules 13a-15(e) and 15d-15(e)) 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) Designed such internal control over financial reporting, or caused such
         internal control over financial reporting to be designed under our
         supervision, to provide reasonable assurance regarding the reliability
         of financial reporting and the preparation of financial statements for
         external purposes in accordance with generally accepted accounting
         principles;

      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 the end
         of the period covered by this annual 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 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 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.

Dated: May 12, 2005

                                            /s/ Nassib G. Chamoun
                                            ----------------------------
                                            Nassib G. Chamoun
                                            Chief Executive Officer