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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)  [Paragraph omitted in accordance with SEC transition instructions
           contained in SEC Release 34-47986]

       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 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 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.

Dated: November 10, 2004

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