Exhibit 32.1

                          CERTIFICATION PURSUANT TO
                           18 U.S.C. SECTION 1350
                     AS ADOPTED PURSUANT TO SECTION 906
                      OF THE SARBANES-OXLEY ACT OF 2002

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 Annual Report on Form 10-K of the Company for the period
            ending June 30, 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: September 28, 2004

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