Ownership Submission
FORM 4
Check this box if no longer subject to Section 16. Form 4 or Form 5 obligations may continue. See Instruction 1(b).
UNITED STATES SECURITIES AND EXCHANGE COMMISSION
Washington, D.C. 20549

STATEMENT OF CHANGES IN BENEFICIAL OWNERSHIP OF SECURITIES

Filed pursuant to Section 16(a) of the Securities Exchange Act of 1934, Section 17(a) of the Public Utility Holding Company Act of 1935 or Section 30(h) of the Investment Company Act of 1940
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(Print or Type Responses)
1. Name and Address of Reporting Person *
MCNAMARA MARTIN B
  2. Issuer Name and Ticker or Trading Symbol
Transocean Ltd. [RIG]
5. Relationship of Reporting Person(s) to Issuer
(Check all applicable)
__X__ Director _____ 10% Owner
_____ Officer (give title below) _____ Other (specify below)
(Last)
(First)
(Middle)
BUILDING F, 7TH FLOOR, CHEMIN DE BLANDONNET 2
3. Date of Earliest Transaction (Month/Day/Year)
05/06/2009
(Street)

VERNIER, V8 1214
4. If Amendment, Date Original Filed(Month/Day/Year)
6. Individual or Joint/Group Filing(Check Applicable Line)
_X_ Form filed by One Reporting Person
___ Form filed by More than One Reporting Person
(City)
(State)
(Zip)
Table I - Non-Derivative Securities Acquired, Disposed of, or Beneficially Owned
1.Title of Security
(Instr. 3)
2. Transaction Date (Month/Day/Year) 2A. Deemed Execution Date, if any (Month/Day/Year) 3. Transaction Code
(Instr. 8)
4. Securities Acquired (A) or Disposed of (D)
(Instr. 3, 4 and 5)
5. Amount of Securities Beneficially Owned Following Reported Transaction(s)
(Instr. 3 and 4)
6. Ownership Form: Direct (D) or Indirect (I)
(Instr. 4)
7. Nature of Indirect Beneficial Ownership
(Instr. 4)
Code V Amount (A) or (D) Price
Ordinary Shares 05/06/2009   M(3)   3,756 A $ 29.68 20,434 D  
Ordinary Shares 05/06/2009   S(3)   2,328 D $ 75.1 18,106 (2) D  

Reminder: Report on a separate line for each class of securities beneficially owned directly or indirectly.
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Table II - Derivative Securities Acquired, Disposed of, or Beneficially Owned
(e.g., puts, calls, warrants, options, convertible securities)
1. Title of Derivative Security
(Instr. 3)
2. Conversion or Exercise Price of Derivative Security 3. Transaction Date (Month/Day/Year) 3A. Deemed Execution Date, if any (Month/Day/Year) 4. Transaction Code
(Instr. 8)
5. Number of Derivative Securities Acquired (A) or Disposed of (D)
(Instr. 3, 4, and 5)
6. Date Exercisable and Expiration Date
(Month/Day/Year)
7. Title and Amount of Underlying Securities
(Instr. 3 and 4)
8. Price of Derivative Security
(Instr. 5)
9. Number of Derivative Securities Beneficially Owned Following Reported Transaction(s)
(Instr. 4)
10. Ownership Form of Derivative Security: Direct (D) or Indirect (I)
(Instr. 4)
11. Nature of Indirect Beneficial Ownership
(Instr. 4)
Code V (A) (D) Date Exercisable Expiration Date Title Amount or Number of Shares
Stock Options $ 29.68 05/06/2009   M     3,756   (1)(3) 05/13/2009 Ordinary Shares 3,756 $ 0 0 D  

Reporting Owners

Reporting Owner Name / Address Relationships
 Director  10% Owner  Officer  Other
MCNAMARA MARTIN B
BUILDING F, 7TH FLOOR
CHEMIN DE BLANDONNET 2
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  X      

Signatures

 Chipman Earle by Power of Attorney   05/08/2009
**Signature of Reporting Person Date

Explanation of Responses:

* If the form is filed by more than one reporting person, see Instruction 4(b)(v).
** Intentional misstatements or omissions of facts constitute Federal Criminal Violations. See 18 U.S.C. 1001 and 15 U.S.C. 78ff(a).
(1) The options are fully vested and exercisable.
(2) On December 19, 2008, Transocean Ltd., a Swiss corporation, became the successor of Transocean Inc., a Cayman Islands company, pursuant to a merger by way of schemes of arrangement under Cayman Islands law (the "Transaction") in which each holder of Transocean Inc. ordinary shares outstanding immediately prior to the Transaction received one registered share of Transocean Ltd. in exchange for each outstanding ordinary share of Transocean Inc. The Transaction had the effect of changing the place of incorporation of Transocean's group holding company from the Cayman Islands to Switzerland but did not alter the proportionate interests of security holders.
(3) The transactions reported in this Form 4, including the exercise of 3,756 options and the related sale of 2,328 registered shares to cover the exercise costs, taxes and commissions, were effected pursuant to a Rule 10b5-1 trading plan.

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