TRANSOCEAN OFFSHORE INC
4, 1997-06-10
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
   LORENTZEN, FRIDTJOF 
   GENERALLUNDEN 7
   OSLO,   0381
   NORWAY
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 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 ( ) Officer (give title below) ( ) Other
   (specify below)
   
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               |5/9/97|S   | |602(1)            |D  |62.83(2)   |                   |I     |(3)                        |
- -----------------------------------------------------------------------------------------------------------------------------------|
Common Stock               |5/9/97|S   | |60(1)             |D  |63.58(2)   |                   |I     |(3)                        |
- -----------------------------------------------------------------------------------------------------------------------------------|
Common Stock               |5/13/9|S   | |542(1)            |D  |63.31(2)   |                   |I     |(3)                        |
                           |7     |    | |                  |   |           |                   |      |                           |
- -----------------------------------------------------------------------------------------------------------------------------------|
Common Stock               |5/14/9|S   | |602(1)            |D  |65.34(2)   |                   |I     |(3)                        |
                           |7     |    | |                  |   |           |                   |      |                           |
- -----------------------------------------------------------------------------------------------------------------------------------|
Common Stock               |5/15/9|S   | |602(1)            |D  |65.80(2)   |                   |I     |(4)                        |
                           |7     |    | |                  |   |           |                   |      |                           |
- -----------------------------------------------------------------------------------------------------------------------------------|
Common Stock               |5/21/9|S   | |901(1)            |D  |65.29(2)   |                   |I     |(5)                        |
                           |7     |    | |                  |   |           |                   |      |                           |
- -----------------------------------------------------------------------------------------------------------------------------------|
Common Stock               |5/22/9|S   | |300(1)            |D  |67.27(2)   |                   |I     |(5)                        |
                           |7     |    | |                  |   |           |                   |      |                           |
- -----------------------------------------------------------------------------------------------------------------------------------|
Common Stock               |5/23/9|S   | |300(1)            |D  |68.68(2)   |167,060            |I     |(5)                        |
                           |7     |    | |                  |   |           |                   |      |                           |
- -----------------------------------------------------------------------------------------------------------------------------------|
Common Stock               |      |    | |                  |   |           |5,599              |D     |                           |
- -----------------------------------------------------------------------------------------------------------------------------------|
___________________________________________________________________________________________________________________________________|
<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)  Represents reporting person's proportionate ownership interest in common 
stock held indirectly through a 
corporation.
(2)  Shares sold in Norwegian Kroner; price shown is Norwegian Kroner price 
converted at the applicable exchange 
rate per U.S. dollar on the date of 
sale.
(3)  Owned indirectly by the reporting person through A/S Filo, A/S Pater and 
Lorentzen Skibs A/S, each a 
Norwegian 
corporation.
(4)  Owned indirectly by the reporting person through A/S Filo and A/S Pater, 
each a Norwegian corporation.
(5)  Owned indirectly by the reporting person through A/S Filo, A/S Pater 
and/or A/S Anilin, each a Norwegian 
corporation.
This Statement confirms that the undersigned, Forrest E. Wylie, 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 is assuming any of the 
undersigned's responsibilities to comply with 
Section 16 of the Securities Exchange Act of 
1934.
Date:  June 10, 1997                                                            
                                          /s/ Fridtjof Lorentzen
                                                                                
                                                       
SIGNATURE OF REPORTING PERSON
/s/ FRIDTJOF LORENTZEN by NICOLAS J. EVANOFF
DATE
JUNE 10, 1997



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