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 31, 2005, 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 13, 2005

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


This certification accompanies this Report on Form 10-Q pursuant to Section
906 of the Sarbanes-Oxley Act of 2002 and shall not, expect to the extent
required by such Act, be deemed filed by the Company for  purposes of
Section 18 of the Securities Exchange Act of 1934, as amended (the
"Exchange Act").  Such certification will not be deemed incorporated by
reference into any filing under the Securities Act of 1933, as amended, or
the Exchange Act, expect to the extent the Company specifically
incorporated it by reference.