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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: August 11, 2004
                                                      /s/ Nassib G. Chamoun
                                                      -------------------------
                                                      Nassib G. Chamoun
                                                      Chief Executive Officer