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                                                                    EXHIBIT 31.1

                                  CERTIFICATION

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

1.   I have reviewed this Quarterly Report on Form 10-Q (the "Report") of the
     registrant;

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 the 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) and internal control over
     financial reporting as defined in Exchange Act Rule 13a-15(f) and
     15d-15(f)) 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 the Report our conclusions about the
          effectiveness of the disclosure controls and procedures, as of the end
          of the period covered by the Report, based on such evaluation; and

     (d)  disclosed in the 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 data; 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: May 4, 2006


                                        /s/ Kevin Conroy
                                        ----------------------------------------
                                        Kevin Conroy,
                                        Chief Executive Officer


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