Exhibit 32.1

                CERTIFICATION OF REGISTRANT'S CHIEF EXECUTIVE
                     OFFICER PURSUANT TO 18 U.S.C. 1350


I, Peter J. Murphy, Chief Executive Officer of Parlex Corporation (the
"Company"), do hereby certify, pursuant to 18 U.S.C. Section 1350, as
adopted pursuant to Section 906 of the Sarbanes-Oxley Act of 2002, that, to
my knowledge:

      (a)   the Quarterly Report on Form 10-Q of the Company for the period
            ending March 28, 2004, as filed with the Securities and Exchange
            Commission (the "Report"), fully complies with the requirements of
            Section 13(a) or 15(d) of the Securities Exchange Act of 1934; and

      (b)   The information contained in the Report fairly presents, in all
            material respects, the financial condition and results of
            operations of the Company.

Dated: May 12, 2004

/s/ Peter J. Murphy
------------------------
Peter J. Murphy
Chief Executive Officer


This certification accompanies this Report pursuant to Section 906 of the
Sarbanes-Oxley Act of 2002 and shall not be deemed filed by the Company for
purposes of Section 18 of the Securities Act of 1934, as amended, or
otherwise subject to liability under that section. This certification shall
not be deemed incorporated by reference in any filing under the Securities
Act or Exchange, except to the extent that the Company specifically
incorporates it by reference.