TRANSOCEAN OFFSHORE INC
4, 1997-09-10
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
   September 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
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               |8/13/9|M   | |13,773            |A  |$21.00     |                   |      |                           |
                           |7     |    | |                  |   |           |                   |      |                           |
- -----------------------------------------------------------------------------------------------------------------------------------|
Common Stock               |8/13/9|S   | |13,773            |D  |$81.22     |                   |      |                           |
                           |7     |    | |                  |   |           |                   |      |                           |
- -----------------------------------------------------------------------------------------------------------------------------------|
Common Stock               |      |    | |                  |   |           |34,163(1)          |D     |                           |
- -----------------------------------------------------------------------------------------------------------------------------------|
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  |     |    | |           |   |(4)  |1/27/|Common Stock|       |       |28,000      |D  |            |
s                     |        |     |    | |           |   |     |04   |            |       |       |            |   |            |
- -----------------------------------------------------------------------------------------------------------------------------------|
Executive Stock Option|$18.50  |     |    | |           |   |(5)  |8/31/|Common Stock|       |       |69,000      |D  |            |
s                     |        |     |    | |           |   |     |04   |            |       |       |            |   |            |
- -----------------------------------------------------------------------------------------------------------------------------------|
Executive Stock Option|$21.00  |8/13/|M   | |13,773     |D  |(6)  |2/23/|Common Stock|13,773 |       |6,887       |D  |            |
s                     |        |97   |    | |           |   |     |05   |            |       |       |            |   |            |
- -----------------------------------------------------------------------------------------------------------------------------------|
Executive Stock Option|$46.875 |     |    | |           |   |(7)  |2/22/|Common Stock|       |       |18,100      |D  |            |
s                     |        |     |    | |           |   |     |06   |            |       |       |            |   |            |
- -----------------------------------------------------------------------------------------------------------------------------------|
Executive Stock Option|$57.50  |     |    | |           |   |(8)  |3/11/|Common Stock|       |       |9,800       |D  |            |
s                     |        |     |    | |           |   |     |07   |            |       |       |            |   |            |
- -----------------------------------------------------------------------------------------------------------------------------------|
                      |        |     |    | |           |   |     |     |            |       |       |            |   |            |
___________________________________________________________________________________________________________________________________|
</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 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.
(5)  Grant of 56,000 options under the LTIP exercisable as follows:  18,667 on 
1/28/95, 18,666 on 1/28/96  and 
18,667 on 
1/28/97.
(6)  Grant of 69,000 options under the LTIP exercisable as follows:  69,000 on 
6/21/95.
(7)  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.
(8)  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.
(9)  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.
SIGNATURE OF REPORTING PERSON
/s/ W. DENNIS HEAGNEY by NICOLAS J. EVANOFF
DATE
September 10, 1997



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