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                                                                    EXHIBIT 32.1

                                  CERTIFICATION

     I, Ronald J. Turner, President and Chief Executive Officer of TC PipeLines
GP, Inc., the general partner of TC PipeLines, LP (the Partnership), in
compliance with 18 U.S.C. Section 1350, as adopted pursuant to Section 906 of
the Sarbanes-Oxley Act of 2002 hereby certify, to the best of my knowledge, in
connection with the Partnership's Quarterly Report on Form 10-Q for the period
ended March 31, 2004 as filed with the Securities and Exchange Commission (the
Report) on the date hereof, that:

     o    the Report fully complies with the requirements of section 13(a) or
          15(d) of the Securities Exchange Act of 1934; and

     o    the information contained in the Report fairly presents, in all
          material respects, the financial condition and results of operations
          of the Partnership.

Dated: May 7, 2004

                                   /s/ Ronald J. Turner
                                   --------------------------------------------
                                   Ronald J. Turner
                                   President and Chief Executive Officer
                                   TC PipeLines GP, Inc., as general partner of
                                   TC PipeLines, LP