TRANSOCEAN OFFSHORE INC
4, 1999-06-14
DRILLING OIL & GAS WELLS
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UNITED STATES SECURITIES AND EXCHANGE COMMISSION
WASHINGTON, D.C. 20549
FORM 4
STATEMENT OF CHANGES IN BENEFICIAL OWNERSHIP
( ) Check this box if no longer subject to Section 16.
Form 4 or Form 5 obligations may continue. See Instructions 1(b).
1. Name and Address of Reporting Person
   Koucouthakis, Barbara S.
   c/o Transocean Offshore Inc.
   4 Greenway Plaza
   Houston, Texas  77046
   USA
2. Issuer Name and Ticker or Trading Symbol
   Transocean Offshore Inc.
   RIG
3. IRS or Social Security Number of Reporting Person (Voluntary)

4. Statement for Month/Year
   May 31, 1999
5. If Amendment, Date of Original (Month/Year)

6. Relationship of Reporting Person(s) to Issuer (Check all applicable)
   ( ) Director ( ) 10% Owner (X) Officer (give title below) ( ) Other
   (specify below)
   Vice President and Controller
7. Individual or Joint/Group Filing (Check Applicable Line)
   (X) Form filed by One Reporting Person
   ( ) Form filed by More than One Reporting Person
<TABLE>
<CAPTION>
___________________________________________________________________________________________________________________________________
 Table I -- Non-Derivative Securities Acquired, Disposed of, or Beneficially Owned                                                 |
___________________________________________________________________________________________________________________________________|
1. Title of Security       |2.    |3.    |4.Securities Acquired (A)         |5.Amount of        |6.Dir |7.Nature of Indirect       |
                           | Transaction |  or Disposed of (D)              |  Securities       |ect   |  Beneficial Ownership     |
                           |      |      |                                  |  Beneficially     |(D)or |                           |
                           |      |    | |                  | A/|           |  Owned at         |Indir |                           |
                           | Date |Code|V|    Amount        | D |    Price  |  End of Month     |ect(I)|                           |
___________________________________________________________________________________________________________________________________|
<S>                        <C>    <C>  <C><C>               <C> <C>         <C>                 <C>    <C>
Ordinary Shares (1)        |5/3/99|D   | |444 (2)           |D  |$30.09     |15,195 (3)         |D     |                           |
- -----------------------------------------------------------------------------------------------------------------------------------|
Ordinary Shares            |      |    | |                  |   |           |1,828              |I     |(4)                        |
- -----------------------------------------------------------------------------------------------------------------------------------|
___________________________________________________________________________________________________________________________________|
<CAPTION>
___________________________________________________________________________________________________________________________________
 Table II -- Derivative Securitites Acquired, Disposed of, or Beneficially Owned                                                   |
___________________________________________________________________________________________________________________________________|
1.Title of Derivative |2.Con-  |3.   |4.    |5.Number of De |6.Date Exer|7.Title and Amount  |8.Price|9.Number    |10.|11.Nature of|
  Security            |version |Transaction | rivative Secu |cisable and|  of Underlying     |of Deri|of Deriva   |Dir|Indirect    |
                      |or Exer |     |      | rities Acqui  |Expiration |  Securities        |vative |tive        |ect|Beneficial  |
                      |cise    |     |      | red(A) or Dis |Date(Month/|                    |Secu   |Securities  |(D)|Ownership   |
                      |Price of|     |      | posed of(D)   |Day/Year)  |                    |rity   |Benefi      |or |            |
                      |Deriva- |     |      |               |Date |Expir|                    |       |ficially    |Ind|            |
                      |tive    |     |      |           | A/|Exer-|ation|   Title and Number |       |Owned at    |ire|            |
                      |Secu-   |     |    | |           | D |cisa-|Date |   of Shares        |       |End of      |ct |            |
                      |rity    |Date |Code|V|  Amount   |   |ble  |     |                    |       |Month       |(I)|            |
___________________________________________________________________________________________________________________________________|
<S>                   <C>      <C>   <C>  <C><C>        <C> <C>   <C>   <C>          <C>     <C>     <C>          <C> <C>
                      |        |     |    | |           |   |     |     |            |       |       |            |   |            |
___________________________________________________________________________________________________________________________________|
</TABLE>
Explanation of Responses:
(1) On May 14, 1999, Transocean Offshore Inc., a Delaware corporation
("Transocean-Delaware"), merged with and  into its wholly owned
subsidiary Transocean Offshore (Texas) Inc., a Texas corporation,  which
survived the merger and immediately thereafter was converted to
and registered by way of continuation as Transocean Offshore Inc., a Cayman
Islands exempted company limited by shares
("Transocean-Cayman").  In the merger and conversion, each share of Common
Stock, par value $.01 per share, of Transocean-Delaware was
converted into one Ordinary Share, par value $.01 per share, of
Transocean-Cayman, including all shares, restricted shares and options to
purchase shares under the  Employee Stock Purchase Plan, Long-Term Incentive
Plan and Savings Plan.  Transocean-Cayman is the successor
issuer to
Transocean-Delaware.
(2) Represents shares acquired and sold under the Transocean Offshore Inc.
Employee Stock Purchase Plan.
(3) Includes unvested restricted shares granted under the Transocean Offshore
Inc. Long-Term Incentive Plan.
(4) Represents shares held under the Transocean Offshore Inc. Savings Plan at
1/31/99.  The number of shares listed is approximate because
Plan accounting is on a unit
basis.
SIGNATURE OF REPORTING PERSON
/s/ Barbara S. Koucouthakis by Nicolas J. Evanoff
DATE
June 11, 1999



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