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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 IN CONNECTION WITH THE
PARTNERSHIP'S ANNUAL REPORT ON FORM 10-K FOR THE YEAR ENDED DECEMBER 31, 2003 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: March 12, 2004                /s/ Ronald J. Turner
                                     ------------------------------------------
                                     Ronald J. Turner
                                     President and Chief Executive Officer
                                     TC PipeLines GP, Inc., as general partner