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
King, Paul A.
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
June 1, 1998
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
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>
Common Stock |5/6/98|M | |8,000 |A |$11.00 | | | |
- -----------------------------------------------------------------------------------------------------------------------------------|
Common Stock |5/6/98|M | |9,600 |A |$8.375 | | | |
- -----------------------------------------------------------------------------------------------------------------------------------|
Common Stock |5/6/98|A | |17,600 |D |$57.4375 |1,900 (1) |D | |
- -----------------------------------------------------------------------------------------------------------------------------------|
Common Stock | | | | | | |721 |I |(2) |
- -----------------------------------------------------------------------------------------------------------------------------------|
___________________________________________________________________________________________________________________________________|
<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>
Executive Stock Option|$11.00 |5/6/9|M | |8,000 |D |(3) |6/30/|Common Stock|8,000 | |0 |D | |
s | |8 | | | | | |03 | | | | | | |
- -----------------------------------------------------------------------------------------------------------------------------------|
Executive Stock Option|$8.375 |5/6/9|M | |9,600 |D |(4) |1/27/|Common Stock|9,600 | |0 |D | |
s | |8 | | | | | |04 | | | | | | |
- -----------------------------------------------------------------------------------------------------------------------------------|
| | | | | | | | | | | | | | |
___________________________________________________________________________________________________________________________________|
</TABLE>
Explanation of Responses:
(1) Includes shares of unvested restricted stock granted under the Transocean
Offshore Inc. Long-Term Incentive Plan ("LTIP").
(2)Shares held under Transocean Offshore Savings Plan at 12/31/97. The number
of shares is approximate because Plan accounting is on a unit
basis.
(3) Grant of 8,000 options under the Long-Term Incentive Plan exercisable as
follows: 2,666 on 6/10/94, 2,666 on 6/10/95 and 2,668 on 6/10/96
(4) Grant of 9,600 options under the Long-Term Incentive Plan exercisable as
follows: 3,200 on 1/28/95, 3,200 on 1/28/96 and 3,200 on 1/28/97.
SIGNATURE OF REPORTING PERSON
/s/ Paul A. King by Nicolas J. Evanoff
DATE
June 11, 1998
