----

**Exhibit      31.1**

**CEO      CERTIFICATION PURSUANT TO SECTION 302 OF THE SARBANES-OXLEY ACT OF      2002**

| 1. | I                have reviewed this quarterly report on Form 10-Q of Transocean                Inc., |
|----|------------------------------------------------------------------------------------------------------|

| 2. | Based                on my knowledge, this quarterly report does not contain any untrue                statement of a material fact or omit to state a material fact necessary                to                make the statements made, in light of the circumstances under which                such                statements were made, not misleading with respect to the period covered                by                this quarterly report; |
|----|--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|

| 3. | Based                on my knowledge, the financial statements, and other financial information                included in this quarterly report, fairly present in all material                respects                the financial condition, results of operations and cash flows of                the                registrant as of, and for, the periods presented in this quarterly                report; |
|----|----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|

| 4. | The                registrant’s other certifying officer and I are responsible for                establishing and maintaining disclosure controls and procedures (as                defined in Exchange Act Rules 13a-15(e) and 15d-15(e)) and internal                control over financial reporting (as defined in Exchange Act Rules                13a-15(f) and 15d-15(f)) for the registrant and we                have: |
|----|-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|

|   | a) | designed                such disclosure controls and procedures, or caused such disclosure                controls and procedures to be designed under our supervision, to                ensure                that material information relating to the registrant, including its                consolidated subsidiaries, is made known to us by others within those                entities, particularly during the period in which this quarterly                report is                being prepared; |
|--------|----|------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|

|   | b) | designed                such internal control over financial reporting, or caused such internal                control over financial reporting to be designed under our supervision,                to                provide reasonable assurance regarding the reliability of financial                reporting and the preparation of financial statements for external                purposes in accordance with generally accepted accounting principles;                and |
|--------|----|--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|

|   | c) | evaluated                the effectiveness of the registrant’s disclosure controls and procedures                and presented in this quarterly report our conclusions about the                effectiveness of the disclosure controls and procedures, as of the                end of                the period covered by this quarterly report based on such evaluation;                and |
|--------|----|---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|

|   | d) | disclosed                in this quarterly report any change in the registrant’s internal control                over financial reporting that occurred during the registrant’s most recent                fiscal quarter (the registrant’s fourth fiscal quarter in the case of an                annual report) that has materially affected, or is reasonably likely                to                materially affect, the registrant’s internal control over financial                reporting; and |
|--------|----|------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|

| 5. | The                registrant’s other certifying officer and I have disclosed, based on our                most recent evaluation of internal control over financial reporting,                to                the registrant’s auditors and the audit committee of registrant’s board of                directors (or persons performing the equivalent                function): |
|----|--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|

|   | a) | all                significant deficiencies and material weaknesses in the design or                operation of internal control over financial reporting which are                reasonably likely to adversely affect the registrant’s ability to record,                process, summarize and report financial information;                and |
|--------|----|------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|

|   | b) | any                fraud, whether or not material, that involves management or other                employees who have a significant role in the registrant’s internal control                over financial reporting. |
|--------|----|-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|

| Date:  | August                2, 2005 | /s/                Robert L. Long                    |
|--------|-------------------------------|------------------------------------------------------|
|   |                          | Robert                L. Long                        |
|   |                          | President                and Chief Executive Officer |

----