Exhibit 32.1

CERTIFICATION PURSUANT TO SECTION 906 OF

THE SARBANES-OXLEY ACT OF 2002 (SUBSECTIONS (a) AND (b)

OF SECTION 1350, CHAPTER 63 OF TITLE 18, UNITED STATES CODE)

Pursuant to Section 906 of the Sarbanes-Oxley Act of 2002 (Subsections (a) and (b) of Section 1350, Chapter 63 of Title 18, United States Code), I, Steven L. Newman, Chief Executive Officer of Transocean Ltd., a Swiss corporation (the “Company”), hereby certify, to my knowledge, that:

(1) the Company’s Annual Report on Form 10-K for the year ended December 31, 2010 (the “Report”) fully complies with the requirements of Section 13(a) or 15(d) of the Securities Exchange Act of 1934; and

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

Dated:           February 28, 2011 /s/ Steven L. Newman                                                                                          Steven L. Newman Chief Executive Officer