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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1. Name and Address of Reporting Person * ANDERSON W RICHARD   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) 10 CHEMIN DE BLANDONNET 3. Date of Earliest Transaction (Month/Day/Year) 05/14/2010 (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 Registered Shares 05/16/2010   M   567 (1) A $ 0 (1) 3,041 D   Registered Shares 05/15/2010   M   1,188 (2) A $ 0 (2) 4,229 D   Registered Shares 05/17/2010   F(3)   238 D (3) 3,991 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

Deferred Units

$ 0 (1)

05/16/2010

M

567

(1)

(1)

Registered Shares

567

$ 0 (1)

567

D

Deferred Units

$ 0 (2)

05/15/2010

M

1,188

(2)

(2)

Registered Shares

1,188

$ 0 (2)

2,377

D

Deferred Units

$ 0 (4)

05/14/2010

A

3,703

(4)

(4)

Registered Shares

3,703

(4)

3,703

D

Reporting Owners

Reporting Owner Name / Address	Relationships
	Director	10% Owner	Officer	Other
ANDERSON W RICHARD 10 CHEMIN DE BLANDONNET VERNIER, V8 1214	X

Signatures

Margaret C. Fitzgerald by Power of Attorney		05/18/2010
**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)	On May 16, 2008, the reporting person was granted 1,701 Deferred Units, which are 1-for-1 registered share equivalents. On May 16, 2010, one third of the award vested per its terms and was paid in registered shares of the issuer per the reporting person's election in 2008 for such Deferred Units to be payable in registered shares upon the earliest of (i) annual vesting of such Deferred Units, (ii) change of control of the issuer or (iii) the reporting person's death, disability or retirement from the Board.
(2)	On May 15, 2009, the reporting person was granted 3,565 Deferred Units, which are 1-for-1 registered share equivalents. On May 15, 2010, one third of the award vested per its terms and was paid in registered shares of the issuer per the reporting person's election in 2009 for such Deferred Units to be payable in registered shares upon the earliest of (i) annual vesting of such Deferred Units, (ii) change of control of the issuer or (iii) the reporting person's death, disability or retirement from the Board.
(3)	Shares automatically withheld upon vesting to satisfy tax withholding obligations.
(4)	Deferred Units, which are 1-for-1 registered share equivalents, were acquired on May 14, 2010 pursuant to the issuer's long-term incentive plan. Deferred Units vest in equal installments on May 14, 2011, 2012 and 2013. The reporting person elected in 2009 for such Deferred Units to be payable in registered shares of the issuer upon the reporting person's death, disability or retirement from the Board.

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