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                                  EXHIBIT 31.1
                                 CERTIFICATIONS

I, Lance Fors, Chief Executive Officer of Third Wave Technologies, Inc. (the
"registrant") certify that:

         1. I have reviewed this Annual Report on Form 10-K of the registrant;

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

         3. Based on my knowledge, the financial statements, and other financial
information included in this annual 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 annual 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 annual report is being prepared;

             (b) evaluated the effectiveness of the registrant's disclosure
         controls and procedures and presented in this annual 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

             (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 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.

                                       By:       /s/ LANCE FORS
                                           --------------------------------
                                                     Lance Fors,
                                             Chief Executive Officer

Date: March 12, 2004