EXHIBIT 31.1

                CERTIFICATION OF REGISTRANT'S CHIEF EXECUTIVE
                     OFFICER REQUIRED BY RULE 13a-14(a)

I, Peter J. Murphy, certify that:

1.    I have reviewed this Quarterly Report on Form 10-Q of Parlex
      Corporation;

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(s) 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.    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

      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 (the registrant's
            fourth fiscal quarter in the case of an annual report) 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(s) 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.

Date: November 12, 2004                /s/ Peter J. Murphy
                                       ------------------------------------
                                       Peter J. Murphy
                                       President & Chief Executive Officer


<PAGE>  41