TRANSOCEAN OFFSHORE INC
4, 1997-07-10
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
   Heagney, W. Dennis
   4 Greenway Plaza
   Houston, TX  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
   July 10, 1997
5. If Amendment, Date of Original (Month/Year)
   
6. Relationship of Reporting Person(s) to Issuer (Check all applicable)
   (X) Director ( ) 10% Owner (X) Officer (give title below) ( ) Other
   (specify below)
   President and Chief Operating Officer
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               |6/3/97|M   | |28,000            |A  |$16.75     |                   |      |                           |
- -----------------------------------------------------------------------------------------------------------------------------------|
Common Stock               |6/3/97|S   | |18,300            |D  |$71.75     |                   |      |                           |
- -----------------------------------------------------------------------------------------------------------------------------------|
Common Stock               |6/3/97|S   | |1,700             |D  |$72.00     |                   |      |                           |
- -----------------------------------------------------------------------------------------------------------------------------------|
Common Stock               |6/3/97|S   | |8,000             |D  |$72.125    |                   |      |                           |
- -----------------------------------------------------------------------------------------------------------------------------------|
Common Stock               |3/12/9|A   |V|2,000(1)          |D  |           |34,163             |D     |                           |
                           |7     |    | |                  |   |           |                   |      |                           |
- -----------------------------------------------------------------------------------------------------------------------------------|
Common Stock               |      |    | |                  |   |           |1,067              |I     |(2)                        |
- -----------------------------------------------------------------------------------------------------------------------------------|
Common Stock               |      |    | |                  |   |           |20                 |I     |(3)                        |
- -----------------------------------------------------------------------------------------------------------------------------------|
___________________________________________________________________________________________________________________________________|
<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|$16.75  |6/3/9|M   | |28,000     |D  |(4)  |1/27/|Common Stock|28,000 |       |28,000      |D  |            |
s                     |        |7    |    | |           |   |     |04   |            |       |       |            |   |            |
- -----------------------------------------------------------------------------------------------------------------------------------|
Executive Stock Option|$18.50  |     |    | |           |   |(5)  |8/31/|Common Stock|69,000 |       |69,000      |D  |            |
s                     |        |     |    | |           |   |     |04   |            |       |       |            |   |            |
- -----------------------------------------------------------------------------------------------------------------------------------|
Executive Stock Option|$21.00  |     |    | |           |   |(6)  |2/23/|Common Stock|20,660 |       |20,660      |D  |            |
s                     |        |     |    | |           |   |     |05   |            |       |       |            |   |            |
- -----------------------------------------------------------------------------------------------------------------------------------|
Executive Stock Option|$46.875 |     |    | |           |   |(7)  |2/22/|Common Stock|18,100 |       |18,100      |D  |            |
s                     |        |     |    | |           |   |     |06   |            |       |       |            |   |            |
- -----------------------------------------------------------------------------------------------------------------------------------|
Executive Stock Option|$57.50  |3/12/|A   |V|9,800      |A  |(8)  |3/11/|Common Stock|9,800  |       |9,800       |D  |            |
s                     |        |97   |    | |           |   |     |07   |            |       |       |            |   |            |
- -----------------------------------------------------------------------------------------------------------------------------------|
                      |        |     |    | |           |   |     |     |            |       |       |            |   |            |
___________________________________________________________________________________________________________________________________|
</TABLE>
Explanation of Responses:
(1) Grant of restricted stock under the Transocean Offshore Inc. Long-Term 
Incentive Plan ("LTIP").  The shares vest 
as follows: 667 on 3/12/00, 667 on 3/12/01 and 666 on 
3/12/02.
(2)  Shares held under the Transocean Offshore Savings Plan at 12/31/96.  The 
number of shares listed is 
approximate because Plan accounting is on a unit 
basis.
(3)  Shares held by my children, as to which I disclaim beneficial 
ownership.
(4)  Grant of 56,000 options under the LTIP exerciseable as follows: 18,667 on 
1/28/95, 18,666 on 1/28/96 and 
18,667 on 
1/28/97.
(5)  Grant of 69,000 options under the LTIP exercisable as follows:  69,000 on 
6/21/95.
(6)  Grant of 20,660 options under the LTIP exercisable as follows:  6,887 on 
2/24/96, 6,886 on 2/24/97 and 6,887 on 
2/24/98.
(7)  Grant of 18,100 options under the LTIP exercisable as follows:  6,033 on 
2/23/97, 6,033 on 2/23/98 and 6,034 on 
2/23/99.
(8)  Grant of 9,800 options under the LTIP exercisable as follows:  3,267 on 
3/12/98, 3,267 on 3/12/99 and 3,266 on 
3/12/2000.
 
This Statement confirms that the undersigned has authorized and designated Eric 
B. Brown and Nicolas J. Evanoff to 
execute and file on the undersigned's behalf all Forms 3, 4 and 5 (including 
any amendments thereto) that the 
undersigned may be required to file with the U.S. Securities and Exchange 
Commission as a result of the 
undersigned's ownership of or transactions in securities of Transocean Offshore 
Inc.  The authority of Eric B. 
Brown and Nicolas J. Evanoff shall continue until the undersigned is no longer 
required to file Forms 3, 4 and 5 with 
regard to securities of Transocean Offshore Inc., unless earlier revoked in 
writing.  The undersigned acknowledges 
that neither Eric B. Brown nor Nicolas J. Evanoff are assuming any of the 
undersigned's responsibilities to comply 
with Section 16 of the Securities Exchange Act of 
1934.
Date:  July 10, 1997                                                            
                                         /s/ W. Dennis Heagney
                                                                                
                                                     
SIGNATURE OF REPORTING PERSON
/s/ W. DENNIS HEAGNEY by NICOLAS J. EVANOFF
DATE
7/10/97



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