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 September 28, 2003, 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:  November 17, 2003

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





19


2