POWER OF ATTORNEY

       Know all by these presents that the undersigned hereby constitutes and appoints each of

Eric B. Brown, Heather G. Callender and Eric J. Christ, signing individually, the undersigned's

true and lawful attorney-in-fact to:

(1) execute for and on behalf of the undersigned, in the undersigned's capacity as an

officer and/or director of Transocean Ltd. (the "Company"), Forms 3, 4 and 5 in

accordance with Section 16(a) of the Securities Exchange Act of 1934 and the

rules thereunder;

(2) do and perform any and all acts for and on behalf of the undersigned which may

be necessary or desirable to complete and execute any such Form 3, 4 or 5 and

timely file such form with the United States Securities and Exchange Commission

and any stock exchange or similar authority; and

(3) take any other action of any type whatsoever in connection with the foregoing

which, in the opinion of such attorney-in-act, may be of benefit to, in the best

interest of or legally required by, the undersigned, it being understood that the

documents executed by such attorney-in-fact on behalf of the undersigned

pursuant to this Power of Attorney shall be in such form and shall contain such

terms and conditions as such attorney-in-fact may approve in such attorney-in-

fact's discretion.

       The undersigned hereby grants to each such attorney-in-fact full power and authority to

do and perform any and every act and thing whatsoever requisite, necessary or proper to be

done in the exercise of any of the rights and powers herein granted, as fully to all intents and

purposes as the undersigned might or could do if personally present, with full power of

substitution or revocation, hereby ratifying and confirming all that such attorney-in-fact, or such

attorney-in-fact's substitute or substitutes, shall lawfully do or cause to be done by virtue of this

power of attorney and the rights and powers herein granted.  The undersigned acknowledges

that the foregoing attorneys-in-fact, in serving in such capacity at the request of the undersigned,

are not assuming, nor is the Company assuming, any of the undersigned's responsibilities to

comply with Section 16 of the Securities Exchange Act of 1934.

       This Power of Attorney shall remain in full force and effect until the undersigned is no

longer required to file Forms 3, 4 and 5 with respect to the undersigned's holdings of and

transactions in securities issued by the Company, unless earlier revoked by the undersigned in a

signed writing delivered to the foregoing attorneys-in-fact.

       IN WITNESS WHEREOF, the undersigned has caused this Power of Attorney to be

executed as of this 17th day of November, 2010.



By:    /s/ Edward R. Muller

Name:  Edward R. Muller