EXHIBIT 32.1

                    CERTIFICATION OF CHIEF EXECUTIVE OFFICER

In connection with the periodic report of Connetics Corporation (the "Company")
on Form 10-Q for the period ended March 31, 2004 as filed with the Securities
and Exchange Commission (the "Report"), I, Thomas G. Wiggans, President and
Chief Executive Officer of the Company, hereby certify as of the date hereof,
solely for purposes of Title 18, Chapter 63, Section 1350 of the United States
Code, that to the best of my knowledge:

         (1)      the Report fully complies with the requirements of Section
                  13(a) or 15(d), as applicable, of the Securities Exchange Act
                  of 1934, and

         (2)      the information contained in the Report fairly presents, in
                  all material respects, the financial condition and results of
                  operations of the Company at the dates and for the periods
                  indicated.

Date: May 10, 2004

/s/ Thomas G. Wiggans
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Thomas G. Wiggans
President and Chief Executive Officer