ENSCO INTERNATIONAL INC
DEF 14A, 1999-05-14
DRILLING OIL & GAS WELLS
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<PAGE>
                                       
                                 SCHEDULE 14A
                                (RULE 14A-101)
                   INFORMATION REQUIRED IN PROXY STATEMENT

                           SCHEDULE 14A INFORMATION

         PROXY STATEMENT PURSUANT TO SECTION 14(A) OF THE SECURITIES 
                             EXCHANGE ACT OF 1934

Filed by the registrant /X/
Filed by a party other than the registrant / /
Check the appropriate box:
/ / Preliminary Proxy Statement
/ / Confidential, for Use of the Commission Only (as permitted by 
    Rule 14a-6(e)(2))
/X/ Definitive Proxy Statement
/ / Definitive Additional Materials
/ / Soliciting Material Pursuant to Section 240.14a - 11(c) or 
    Section 240.14a-12
                                       
                       ENSCO International Incorporated
- -------------------------------------------------------------------------------
               (Name of Registrant as Specified in Its Charter)

- -------------------------------------------------------------------------------
   (Name of Person(s) Filing Proxy Statement, if other than the Registrant)

Payment of filing fee (Check the appropriate box):
    /X/ No Fee Required.
    / / Fee computed on table below per Exchange Act Rules 14a-6(i)(4) and 0-11.

    (1)  Title of each class of securities to which transaction applies:

- -------------------------------------------------------------------------------
    (2)  Aggregate number of securities to which transaction applies:

- -------------------------------------------------------------------------------
    (3)  Per unit or other underlying value of transaction computed pursuant to
         Exchange Act Rule 0-11 (Set forth the amount on which the filing fee
         is calculated and state how it was determined):

- -------------------------------------------------------------------------------
    (4)  Proposed maximum aggregate value of transaction:

- -------------------------------------------------------------------------------
    (5)  Total fee paid:

- -------------------------------------------------------------------------------
    / / Fee paid previously with preliminary materials.

/ / Check box if any part of the fee is offset as provided by Exchange Act
Rule 0-11(a)(2) and identify the filing for which the offsetting fee was paid
previously.  Identify the previous filing by registration statement number, or
the Form or Schedule and the date of its filing.

    (1)  Amount Previously Paid:

- -------------------------------------------------------------------------------
    (2)  Form, Schedule or Registration Statement No.:

- -------------------------------------------------------------------------------
    (3)  Filing Party:

- -------------------------------------------------------------------------------
    (4)  Date Filed:
                                          
- -------------------------------------------------------------------------------

<PAGE>
                                       
                                  [ENSCO LOGO]

CARL F. THORNE
CHAIRMAN, PRESIDENT AND CHIEF EXECUTIVE OFFICER

                                   
                                   March 26, 1999
                                        


DEAR FELLOW STOCKHOLDER:
     
     On behalf of our Board of Directors, I cordially invite you to attend 
the 1999 Annual Meeting of Stockholders of ENSCO International Incorporated 
(the "Company").  The Annual Meeting will be held at 10:00 a.m. on Tuesday, 
May 18, 1999 at the Fairmont Hotel, 1717 N. Akard, Dallas, Texas.  Your Board 
of Directors and Officers look forward to greeting personally those 
stockholders able to attend.

     At the Annual Meeting, stockholders will be asked to vote on the 
election of three Class II Directors and to approve the appointment of the 
Company's independent accountants.  Each of the matters to be considered at 
the Annual Meeting is described in detail in the attached Proxy Statement for 
the Annual Meeting.  Your Board of Directors recommends that you vote "For" 
the proposals on the agenda.

     Your vote is important.  Whether or not you are able to attend the 
Annual Meeting, I hope you will promptly sign and date the enclosed proxy 
card and return it in the enclosed postage prepaid envelope.  This will save 
your Company additional expenses associated with soliciting proxies, as well 
as ensure that your shares are represented.  Please note that you may vote in 
person at the Annual Meeting even if you have previously returned the proxy.

                                   Sincerely,

                                   /s/ Carl F. Thorne

                                   Carl F. Thorne

<PAGE>
                                       
                       ENSCO INTERNATIONAL INCORPORATED
                            2700 FOUNTAIN PLACE
                              1445 ROSS AVENUE
                          DALLAS, TEXAS 75202-2792
                              (214) 922-1500

                   NOTICE OF ANNUAL MEETING OF STOCKHOLDERS

                          TO BE HELD ON MAY 18, 1999

     The Annual Meeting of Stockholders of ENSCO International Incorporated 
(the "Company") will be held at the Fairmont Hotel, 1717 N. Akard, Dallas, 
Texas, at 10:00 a.m., Dallas time, on Tuesday, May 18, 1999, to consider and 
vote on:

     1.   The election of three Class II Directors, each for a three-year 
          term;

     2.   The approval of the appointment of PricewaterhouseCoopers LLP as the
          Company's independent accountants for 1999; and

     3.   Such other business as may properly come before the Annual Meeting.

     Stockholders of record at the close of business on March 25, 1999, are 
entitled to notice of and to vote at the Annual Meeting or any adjournment 
thereof.  A list of all stockholders entitled to vote at the Annual Meeting 
is on file at the executive offices of the Company, 2700 Fountain Place, 1445 
Ross Avenue, Dallas, Texas 75202-2792.

                                   By Order of the Board of Directors

                                   /s/ William S. Chadwick, Jr.

                                   William S. Chadwick, Jr.
                                   Vice President and Secretary


March 26, 1999
                                       
          YOUR VOTE IS IMPORTANT.  PLEASE SIGN, DATE AND RETURN THE
                         ACCOMPANYING PROXY PROMPTLY.

                                       1
<PAGE>

                       ENSCO INTERNATIONAL INCORPORATED
                                          
                               PROXY STATEMENT


     The following information is submitted concerning the enclosed Proxy and 
the matters to be acted upon under the authority thereof at the Annual 
Meeting of Stockholders (the "Annual Meeting") of ENSCO International 
Incorporated (the "Company") to be held at the Fairmont Hotel, 1717 N. Akard, 
Dallas, Texas, on Tuesday, the 18th day of May, 1999 at 10:00 a.m., Dallas 
time, or any adjournment thereof, pursuant to the enclosed Notice of Annual 
Meeting of Stockholders.  This Proxy Statement and the enclosed Proxy are 
first being sent on or about March 26, 1999 to holders of the Company's 
shares of capital stock entitled to vote at the Annual Meeting (the 
"Stockholders").
                                       
                                VOTING AND PROXY

     The enclosed Proxy is solicited on behalf of the Board of Directors of 
the Company.  It may be revoked by a Stockholder at any time prior to the 
exercise thereof by filing with the Secretary of the Company a written 
revocation or duly executed Proxy bearing a later date.  The Proxy shall also 
be revoked if a Stockholder is present at the Annual Meeting and elects to 
vote in person.

     Unless contrary instructions are indicated, all shares represented by 
validly executed Proxies received pursuant to this solicitation (and which 
have not been revoked before they are voted) will be voted:

     1.   FOR the election of the Class II nominees for Directors named herein;

     2.   FOR the approval of the appointment of PricewaterhouseCoopers LLP as
          the Company's independent accountants for 1999; and 

     3.   In accordance with the recommendation of management as to any other
          matters which may properly come before the Annual Meeting.

     In the event a Stockholder specifies a different choice by means of the 
enclosed Proxy, his/her shares will be voted in accordance with the 
specification so made.

     The cost of solicitation of proxies will be borne by the Company and, 
upon request, the Company will reimburse brokers, dealers, banks and 
trustees, or their nominees, for reasonable expenses incurred by them in 
forwarding proxy material to and solicitation of proxies from beneficial 
owners of the Company's common stock, par value $.10 per share ("Common 
Stock").  In addition to the use of mail, regular employees or agents of the 
Company may solicit proxies by telephone, telegram or other means of 
communication. 

                                       2
<PAGE>

                        VOTING SECURITIES OUTSTANDING

     The Stockholders entitled to vote at the Annual Meeting are the holders 
of record at the close of business on March 25, 1999 (the "Record Date") of 
approximately 137,047,000 outstanding shares of Common Stock.   Each 
outstanding share of Common Stock is entitled to one vote on each matter to 
come before the Annual Meeting.  A list of all Stockholders entitled to vote 
is on file at the executive offices of the Company, 2700 Fountain Place, 1445 
Ross Avenue, Dallas, Texas 75202-2792.  Only Stockholders of record on the 
books of the Company on the Record Date will be entitled to vote at the 
Annual Meeting.

     For purposes of conducting the Annual Meeting, the holders of at least a 
majority of the stock issued and outstanding and entitled to vote at the 
Annual Meeting shall constitute a quorum.  A holder of stock shall be treated 
as being present at the Annual Meeting if the holder of such stock is (i) 
present in person at the Annual Meeting or (ii) represented at the Annual 
Meeting by a valid proxy, whether the instrument granting such proxy is 
marked as casting a vote or abstaining, is left blank or does not empower 
such proxy to vote with respect to some or all matters to be voted upon at 
the Annual Meeting.  If a quorum is not present or represented at the Annual 
Meeting, the Chairman of the Board of Directors or the Stockholders holding a 
majority of the Common Stock present at the Annual Meeting have the power to 
adjourn the Annual Meeting from time to time, without notice other than an 
announcement at the Annual Meeting. Each proposal being submitted to 
Stockholders for approval shall be approved if the votes cast in favor of 
such proposal exceed the votes cast opposing such proposal.  The Company's 
Bylaws include provisions specifically addressing the treatment of 
abstentions and non-votes by brokers.  In determining the number of votes 
cast, shares abstaining from voting on a matter and shares that are indicated 
as not being voted on a matter by brokers due to lack of discretionary 
authority will not be treated as votes cast with respect to Proposals 1 and  
2. 
                                       
                        OWNERSHIP OF VOTING SECURITIES

     The following tables set forth certain information concerning the number 
of shares of Common Stock owned beneficially as of February 28, 1999, by (i) 
each person known to the Company to own more than 5 percent of the Common 
Stock (the only class of voting securities outstanding); (ii) each director 
of the Company including employee directors; (iii) the three other most 
highly compensated executive officers of the Company who are not also 
directors and (iv) all directors and executive officers of the Company as a 
group.
                                       
                             BENEFICIAL OWNER TABLE

<TABLE>
<CAPTION>
                                             BENEFICIAL OWNERSHIP(1)
        NAME AND ADDRESS                   ---------------------------
     OF BENEFICIAL OWNER(2)                AMOUNT           PERCENTAGE
     ----------------------                ------           ----------
<S>                                     <C>                 <C>
FMR Corp.
    82 Devonshire
    Boston, MA 02109                    17,888,910(3)          13.1%
     
Richard E. Rainwater
    777 Main Street, Suite 2100
    Fort Worth, TX 76102                 7,374,160(4)           5.4%
</TABLE>

                                       3
<PAGE>

DIRECTORS AND EXECUTIVE OFFICERS:       

<TABLE>
<CAPTION>
                                             BENEFICIAL OWNERSHIP(1)
        NAME AND ADDRESS                   ---------------------------
       OF BENEFICIAL OWNER                AMOUNT           PERCENTAGE
       -------------------                ------           ----------
<S>                                     <C>                 <C>
Carl F. Thorne
     Chairman, President and
     Chief Executive Officer            1,881,877(5)            1.4%
                                        
Morton H. Meyerson
     Director                             433,163(6)             --(7)
                                        
Richard A. Wilson
     Director, Senior Vice President and 
     Chief Operating Officer              197,384(8)             --(7)
                                        
C. Christopher Gaut
     Vice President - Finance and
     Chief Financial Officer              238,830(9)             --(7)
                                        
William S. Chadwick, Jr.
     Vice President - Administration and
     Secretary                            198,587(10)            --(7)
                                        
Dillard S. Hammett
     Director                             106,101(11)            --(7)

Marshall Ballard
     Vice President - Business 
     Development                          147,451(12)            --(7)
                                        
Orville D. Gaither, Sr.
     Director                              79,259(13)            --(7)
                                        
Thomas L. Kelly II
     Director                              68,437(14)            --(7)
                                        
Craig I. Fields
     Director                              42,259(15)            --(7)
                                        
Gerald W. Haddock
     Director                              19,553(16)            --(7)
                                        
All Directors and Executive 
 Officers as a Group (14 persons, 
 including those named above)           3,660,734(17)             2.7%
</TABLE>

- ---------------------
(1)    At February 28, 1999, there were 137,047,152 shares of Common Stock
       outstanding.  Unless otherwise indicated, each person or group has sole
       voting and dispositive power with respect to all shares.

(2)    Princeton Services, Inc., Merrill Lynch Asset Management, L.P., Merrill
       Lynch & Co., Inc. and Merrill Lynch Growth Fund advised the Company that
       they divested their holdings of the shares of Common Stock reported on
       Amendment No. 7 to Schedule 13G dated January 8, 1999.

                                       4
<PAGE>

(3)    Based upon information obtained from FMR Corp. as of February 28, 1999,
       FMR Corp. may be deemed to be the beneficial owner of 17,888,910 shares
       of Common Stock.
          
(4)    Based upon information supplied by Richard E. Rainwater's attorney, Mr.
       Rainwater may be deemed to be the beneficial owner of 7,374,160 shares
       of Common Stock.  Includes 893,600 shares held by the Richard E.
       Rainwater Charitable Remainder Unitrust No. 1, of which Mr. Rainwater is
       sole trustee, and also includes 16,200 shares held by Mr. Rainwater's
       spouse, as to all of which Mr. Rainwater disclaims beneficial ownership. 
       Does not include 783,054 shares held by Mr. Rainwater's adult children,
       as to all of which Mr. Rainwater disclaims beneficial ownership.

(5)    Includes 300,000 shares of restricted stock which vest at the rate of
       150,000 shares per annum over a 10-year term, which commenced November
       19, 1990.  The restricted stock grant was approved by the Stockholders
       at the Annual Meeting held on June 5, 1990.  Also includes 100,000
       shares immediately issuable upon exercise of options and 4,478 shares
       held indirectly under the ENSCO Savings Plan and Supplemental Executive
       Retirement Plan ("SERP").
       
(6)    Includes 6,000 shares immediately issuable upon exercise of options and
       230,000 shares of Common Stock beneficially owned by various trusts as
       to all of which Mr. Meyerson disclaims beneficial ownership.
       
(7)    Ownership is less than one percent of the shares of Common Stock
       outstanding.
       
(8)    Includes 71,000 shares immediately issuable upon exercise of options and
       38,000 shares of restricted stock of which 24,000 vest at the rate of
       4,000 per annum and 14,000 of which vest at the rate of 2,000 per annum. 
       Also includes 2,221 shares held indirectly under the ENSCO Savings Plan
       and SERP.
       
(9)    Includes 60,873 shares immediately issuable upon exercise of options and
       33,000 shares of restricted stock of which 7,000 vest at the rate of
       3,500 per annum, 12,000 vest at the rate of 2,000 per annum and 14,000
       vest at the rate of 2,000 per annum.  Also includes 2,009 shares held
       indirectly under the ENSCO Savings Plan and SERP and 2,400 shares gifted
       under TUGMA to minor children for which Mr. Gaut disclaims beneficial
       ownership.
       
(10)   Includes 80,500 shares immediately issuable upon exercise of options and
       34,000 shares of restricted stock of which 12,000 vest at the rate of
       2,000 per annum, 14,000 vest at the rate of 2,000 per annum and 8,000
       vest at the rate of 1,000 per annum.  Also includes 3,192 shares held
       indirectly under the ENSCO Saving Plan and SERP.
       
(11)   Includes 18,000 shares immediately issuable upon exercise of options.
       
(12)   Includes 49,500 shares immediately issuable upon exercise of options and
       7,000 shares of restricted stock which vests at the rate of 1,000 per
       annum.  Also includes 3,500 shares owned by Mr. Ballard's wife, in
       respect of which Mr. Ballard disclaims beneficial ownership, and 1,982
       shares held indirectly under the ENSCO Savings Plan and SERP.
       
(13)   Includes 63,000 shares immediately issuable upon exercise of options.
       
(14)   Includes 18,000 shares immediately issuable upon exercise of options.
       
(15)   Includes 18,000 shares immediately issuable upon exercise of options.

(16)   Includes 18,000 shares immediately issuable upon exercise of options.

(17)   Includes all shares owned individually by the Company's executive
       officers and directors, including 230,000 shares beneficially owned by
       various trusts established by Mr. Meyerson, 3,500 shares owned by Mr.
       Ballard's wife,  2,400 shares gifted under TUGMA to minor children of
       Mr. Gaut,  600,619 shares issuable upon exercise of options, 455,000
       shares of restricted stock, and 22,026 shares held indirectly under the
       ENSCO Savings Plan and SERP.

                                       5
<PAGE>

                                     PROPOSAL 1

                               ELECTION OF DIRECTORS


     The Company's Amended and Restated Certificate of Incorporation provides 
that the Board of Directors of the Company is divided or "classified", with 
respect to the time for which they individually hold office, into three 
classes ("Classes I, II and III"), consisting of, as nearly as possible, one 
third of the entire Board.  The Company's Board of Directors is currently 
fixed at eight members.  Each director holds office for a term ending on the 
date of the third annual meeting following the annual meeting at which such 
director was elected. The current term for Class II Directors will expire at 
the 1999 Annual Meeting of Stockholders.  The current term for Class I and 
Class III Directors will expire at the 2000 and 2001 Annual Meetings of 
Stockholders, respectively.

     Three persons are nominated for election as Class II Directors at the
Annual Meeting.  The Board of Directors urges you to vote FOR the election of
the individuals who have been nominated to serve as Class II Directors.  It is
intended that each validly executed proxy solicited hereby will be voted FOR the
election of the nominees for Class II Directors listed below, unless a contrary
instruction has been indicated on such proxy.  If, at the time of the Annual
Meeting, any of the nominees should be unable or decline to serve, the
discretionary authority provided in the Proxy will be used to vote for a
substitute or substitutes as may be designated by the Board of Directors.  The
Board of Directors has no reason to believe that any substitute nominee or
nominees will be required.

NOMINEES

CLASS II DIRECTORS

CRAIG I. FIELDS; AGE 52; CHAIRMAN, DEFENSE SCIENCE BOARD

     Dr. Fields has been a director of the Company since March 1992.  He assumed
his current position with The Defense Science Board in 1995.  He served as Vice
Chairman with Alliance Gaming Corporation from September 1994 to June 1997. 
From 1990 through August 1994, Dr. Fields was Chairman and Chief Executive
Officer of Microelectronics and Computer Technology Corp.  Between 1974 and
1990, Dr. Fields served the Defense Advanced Research Projects Agency, a
research division of the office of the Secretary of Defense, as a director and
currently serves as a director of Network Solutions, Inc., Firearms Training
Systems, Inc., Enso Audio Imaging Corp., Global Integrity Corp. and Muzak, Inc.
Dr. Fields holds a Bachelor of Science Degree in Physics from the Massachusetts
Institute of Technology and a Ph.D. from Rockefeller University.  He lives in
Washington D.C.  Dr. Fields is a member of the Audit Committee.

MORTON H. MEYERSON; AGE 60; CHAIRMAN AND CHIEF EXECUTIVE OFFICER, 2M COMPANIES,
INC.

     Mr. Meyerson has been a director of the Company since September 1987.  
Mr. Meyerson is currently Chairman and Chief Executive Officer of 2M 
Companies, Inc. He served as Chairman of the Board of Perot Systems from 
September 1996 until November 1997.  In addition, from June 1992 until 
September 1996 and from July 1997 until November 1997, Mr. Meyerson served as 
Chief Executive Officer of Perot Systems.  From May 1986 until June 1992, Mr. 
Meyerson was a private investor.  Mr. Meyerson serves as Vice Chairman of the 
National Parks Foundation, and is a director of Crescent Real Estate 
Equities, Inc. and Optimark Technologies, Inc.  Mr. Meyerson holds Bachelor 
of Arts Degrees in Economics and Philosophy from the University of Texas.  He 
lives in Dallas, Texas.  Mr. Meyerson is Chairman of the Nominating and 
Compensation Committee.


                                       6
<PAGE>

RICHARD A. WILSON; AGE 61; SENIOR VICE PRESIDENT AND CHIEF OPERATING OFFICER OF
THE COMPANY

     Mr. Wilson has been a director of the Company since June 1990.  Mr. Wilson
joined the Company in July 1988 and was elected President of ENSCO Drilling
Company, a wholly-owned subsidiary of the Company, in August 1988 and currently
serves as President of all ENSCO drilling subsidiaries.  Mr. Wilson was elected
Senior Vice President - Operations of the Company in October 1989 and to his
present position in June 1991.  Mr. Wilson holds a Bachelor of Science Degree in
Petroleum Engineering from the University of Wyoming.

      THE BOARD OF DIRECTORS RECOMMENDS THAT STOCKHOLDERS VOTE "FOR" THE
     ELECTION OF EACH OF THE NOMINEES FOR CLASS II DIRECTORS NAMED ABOVE.


CONTINUING DIRECTORS

CLASS I DIRECTORS

GERALD W. HADDOCK; AGE 51; PRESIDENT AND CHIEF EXECUTIVE OFFICER, CRESCENT REAL
ESTATE EQUITIES COMPANY AND CRESCENT OPERATING, INC.

     Mr. Haddock has been a director of the Company since December 1986.  He has
served as Chief Executive Officer of Crescent Real Estate Equities Company since
December 1996.  He has served as director or trust manager of that company since
May 1994 and was Chief Operating Officer from May 1994 until December 1996. 
Since April 1997, Mr. Haddock has served as the President and Chief Executive
Officer of Crescent Operating, Inc.  He has served as a director of that company
since April 1997.  Mr. Haddock holds a Bachelor of Business Administration
Degree from Baylor University, a Juris Doctorate Degree from Baylor University
College of Law and a Master of Taxation Degree from New York University. He
lives in Fort Worth, Texas.  Mr. Haddock is Chairman of the Audit Committee.

CARL F. THORNE; AGE 58; CHAIRMAN, PRESIDENT AND CHIEF EXECUTIVE OFFICER OF THE
COMPANY

     Mr. Thorne has been a director of the Company since December 1986.  He was
elected President and Chief Executive Officer of the Company in May 1987 and was
elected Chairman of the Board of Directors in November 1987.  Mr. Thorne
presently serves as a director of Crescent Operating, Inc., where he is
currently Chairman of the Compensation Committee and a member of the Audit
Committee.  Mr. Thorne holds a Bachelor of Science Degree in Petroleum
Engineering from The University of Texas and a Juris Doctorate Degree from
Baylor University College of Law.  He lives in Dallas, Texas.

CLASS III DIRECTORS

ORVILLE D. GAITHER, SR.; AGE 72; CHAIRMAN, GAITHER PETROLEUM CORPORATION

     Mr. Gaither has been a director of the Company since March 1992.  Mr.
Gaither has served as Chairman and Chief Executive Officer of Gaither Petroleum
Corporation since May 1991, and also held the position of President of that
organization from May 1991 until September 1997.  Prior to May 1991, Mr. Gaither
was employed by Amoco Production Company for 42 years, most recently as
President of the Africa and Middle East Region, responsible for Amoco's
petroleum operations in 17 countries.  Mr. Gaither is on the Board of Directors
of the Sam Houston Area Council of the Boy Scouts of America and a member of the
Advisory Board of Rice University's George R. Brown School of Engineering. Mr.
Gaither holds a Bachelor of Science Degree in Mechanical Engineering from Rice
University, a Master of Science Degree in Petroleum Engineering from the
University of Houston and is a graduate of the Senior Executive Program of
Stanford University.  He lives in Houston, Texas.  Mr. Gaither is a member of
the Nominating and Compensation Committee.


                                       7
<PAGE>

DILLARD S. HAMMETT; AGE 68; CONSULTANT

     Mr. Hammett has been a director of the Company since September 1987.  From
July 1987 to December 1991, Mr. Hammett was Vice President - Technical and
Marketing of the Company.  In January 1992, Mr. Hammett took a leave of absence
from his Vice President position and retired from the Company in December 1992. 
Mr. Hammett holds a Bachelor of Science Degree in Civil Engineering from the
University of Oklahoma.  He lives in Dallas, Texas.  Mr. Hammett is a member of
the Audit Committee.


THOMAS L. KELLY II; AGE 40; GENERAL PARTNER OF CHB CAPITAL PARTNERS

Mr. Kelly has been a director of the Company since September 1987.  He has been
a General Partner of CHB Capital Partners since July 1994.  From May 1987
through June 1994, Mr. Kelly was a private investor.  Mr. Kelly holds a Bachelor
of Arts Degree in Economics and a Bachelor of Science Degree in Administrative
Science from Yale University and a Master of Business Administration Degree from
Harvard University.  He lives in Denver, Colorado.  Mr. Kelly is a member of the
Nominating and Compensation Committee.

                         MEETINGS AND COMMITTEES OF THE BOARD

BOARD OF DIRECTORS

     The Board of Directors met four times during the year ended December 31,
1998 and acted three times by unanimous written consent.  During 1998, each
incumbent director attended 75% or more of the meetings held by the Board and
the committees of which he was a member.  The Board of Directors has two
standing committees: the Audit Committee and the Nominating and Compensation
Committee.

AUDIT COMMITTEE

     The Company's Audit Committee recommends a firm of independent accountants
to examine the consolidated financial statements of the Company, reviews the
general scope of services to be rendered by the independent accountants, reviews
the financial condition and results of operations of the Company and makes
inquiries as to the adequacy of the Company's financial and accounting controls.
The Audit Committee met three times in 1998.  The Committee consists of Chairman
Gerald W. Haddock, Craig I. Fields and Dillard S. Hammett.

NOMINATING AND COMPENSATION COMMITTEE

     The principal functions of the Nominating and Compensation Committee are to
recommend officers of the Company, to select nominees for the Board of Directors
and committees of the Board and to review and approve employee compensation
matters, including matters regarding the Company's various benefit plans.  The
names of potential director candidates are drawn from a number of sources,
including recommendations from members of the Board, management and
stockholders.  Stockholders wishing to recommend Board nominees should submit
their recommendations in writing to the Secretary of the Company, with the
submitting Stockholder's name and address and pertinent information about the
proposed nominee similar to that set forth for the nominees named herein.  A
Stockholder intending to nominate an individual as a director at an annual
meeting, rather than recommend the individual to the Company for consideration
as a nominee, must comply with the advance notice requirements set forth in the
Company's Bylaws.  The Nominating and Compensation Committee met four times
during 1998 and acted once by unanimous written consent.  The Committee consists
of Chairman Morton H. Meyerson, Orville D. Gaither, Sr. and Thomas L. Kelly II.


                                       8
<PAGE>

COMPENSATION OF NON-EMPLOYEE DIRECTORS

     Each non-employee director receives annual compensation of $24,000 per
year, payable quarterly, one-half in cash and one-half in shares of Common
Stock.  Additionally, each non-employee director receives $1,000 in cash for
each Board of Directors and committee meeting attended.  Any non-employee
director that serves the Company as Chairman of the Board of Directors, Chairman
of the Nominating and Compensation Committee or Chairman of the Audit Committee
also receives an additional $500 in cash for each meeting at which the director
acts as Chairman.  Non-employee directors are also eligible to participate in
the Company's group medical and dental insurance plan on the same basis as 
full-time Company employees.  A non-employee director's contribution to group 
medical and dental insurance premium costs is withheld from the quarterly 
payments of the director's annual retainer.  Directors who are also employees 
of the Company do not receive any additional compensation for their services 
as directors.

     Under the ENSCO International Incorporated 1998 Incentive Plan, the number
of shares of Common Stock issued quarterly as part of the annual compensation to
each non-employee director is determined by dividing into $3,000 the average of
the high and low prices of the Common Stock on the New York Stock Exchange on
the first business day of each quarter.  Thus, in 1998 Messrs. Fields, Gaither,
Haddock, Hammett, Kelly and Meyerson each received 633 shares of Common Stock at
an average price of between $11.22 and $33.09 per share.  

     In May 1996, the Stockholders approved the Company's 1996 Non-Employee
Directors' Stock Option Plan ("Directors' Plan") which was adopted by the Board
of Directors on February 21, 1996.  Under the Directors' Plan, 600,000 shares of
Common Stock are reserved for issuance.  Pursuant to the Directors' Plan, 
non-employee directors are granted options to purchase shares of Common Stock 
as follows:  (a) each non-employee director elected after February 21, 1996 
who has not previously served as a director shall be granted an option, 
effective as of the date of the annual stockholders meeting at which such 
director is elected to purchase 15,000 shares of Common Stock and (b) each 
other non-employee director elected at, or continuing to serve following, 
each annual Stockholders meeting, commencing with the 1996 Annual Meeting, 
shall be granted an option to purchase 6,000 shares of Common Stock.  Each of 
Messrs. Fields, Gaither, Haddock, Hammett, Kelly and Meyerson was granted 
options to purchase 6,000 shares of Common Stock on May 13, 1998 at an 
exercise price of $29.3125 per share.  Each shall receive on May 19, 1999 an 
option to purchase 6,000 shares at an exercise price per share equal to the 
average of the high and low selling price of Common Stock on that date.  Such 
awards for Messrs. Fields and Meyerson are subject to their re-election.

     Apart from his duties as a director of the Company, in 1998 Mr. Hammett
provided consulting services to the Company in connection with its construction
of the semisubmersible drilling rig.  Mr. Hammett was paid a discretionary bonus
of $240,000 for these services, of which $120,000 was paid in the third quarter
of 1998 and $120,000 was paid in the first quarter of 1999.

                                EXECUTIVE COMPENSATION

     The following table sets forth a summary of all compensation, including
cash and other forms of remuneration, paid through March 1, 1999, for services
rendered in all capacities to the Company during 1998, to the Chief Executive
Officer and the four other most highly compensated executive officers of the
Company as to whom the total cash compensation paid through such date exceeded
$100,000.  The table also includes a summary of all compensation, including cash
and other forms of remuneration, paid to these named individuals for the years
1997 and 1996.


                                       9

<PAGE>
<TABLE>
                                                    SUMMARY COMPENSATION TABLE
<CAPTION>
                                                  ANNUAL COMPENSATION                 LONG TERM COMPENSATION
                                          ---------------------------------    ------------------------------------
                                                                                       AWARDS              PAYOUTS
                                                                               ----------------------      --------
                                                                     OTHER                                                 ALL
                                                                    ANNUAL     RESTRICTED                                 OTHER
                                                                    COMPEN-       STOCK                     LTIP          COMPEN-
      NAME AND PRINCIPAL                  SALARY       BONUS        SATION        AWARD       OPTIONS      PAYOUTS        SATION
          POSITION               YEAR       ($)       ($)(1)        ($)(2)       ($)(3)       (#)(4)        ($)(5)        ($)(6)
- -------------------------------  ----     -------     -------      -------     ----------     -------      --------       -------
<S>                              <C>      <C>         <C>          <C>         <C>            <C>          <C>            <C>
Carl F. Thorne                   1998     487,500     362,268         N/A          N/A            N/A         N/A         81,653
  President and                  1997     450,000     482,930         N/A          N/A        200,000         N/A         74,935
  Chief Executive Officer        1996     405,000     408,747         N/A          N/A            N/A         N/A         30,521
                                                                                                                                
Richard A. Wilson                1998     283,250     125,682         N/A          N/A            N/A         N/A         48,966
  Senior Vice President and      1997     250,000     207,883         N/A          N/A        200,000         N/A         32,715
  Chief Operating Officer        1996     211,500     188,410         N/A          N/A            N/A         N/A         20,627

C. Christopher Gaut              1998     210,000     149,979         N/A          N/A            N/A         N/A         29,753
  Vice President - Finance       1997     187,500     168,563         N/A          N/A        150,000         N/A         21,150
  and Chief Financial            1996     167,250     160,168         N/A          N/A            N/A         N/A         16,837
  Officer

Marshall Ballard                 1998     205,000      90,892         N/A          N/A            N/A         N/A         32,879
  Vice President -               1997     190,000     133,845         N/A          N/A        100,000         N/A         23,897
  Business Development           1996     172,800      53,046         N/A          N/A            N/A         N/A         18,253
                                                                                                                                
William S. Chadwick, Jr.         1998     194,750     125,000         N/A          N/A            N/A         N/A         28,222
  Vice President -               1997     175,000     155,903         N/A          N/A        100,000         N/A         19,508
  Administration and             1996     147,250     147,152         N/A      148,125            N/A         N/A         16,315
  Secretary
</TABLE>

- -----------------
N/A - Not Applicable.

(1)  Bonuses are awarded in February based on the Company's performance in the
     previous year.  Bonuses are payable as follows:  50% of the amount awarded
     is paid in February of the year in which the award was made, and the
     remainder is payable in two equal installments during February of the two
     subsequent years,  provided the officer remains employed by the Company at
     such date.

(2)  The aggregate amount of perquisites and other personal benefits for any
     named executive does not exceed $50,000 or 10% of the total annual salary
     and bonus for any such named executive and is, therefore, not reflected in
     the table.

(3)  The amounts disclosed in this column, if any, represent the value of
     restricted stock awards on the date of grant. The restricted stock awards
     have vesting schedules of ten years and vest based on the passage of time
     and the continued employment of the named executive.  The total number of
     shares of unvested restricted stock held as of December 31, 1998, and the
     value of such shares, based on the closing price of the Common Stock at
     December 31, 1998 of $10.6875, is as follows: Mr. Thorne, 300,000 shares
     ($3,206,250), all of which vest at the rate of 150,000 shares per annum;
     Mr. Wilson, 38,000 shares ($406,125), 24,000 of which vest at the rate of
     4,000 per annum and 14,000 of which vest at the rate of 2,000 per annum;
     Mr. Gaut, 33,000 shares ($352,688), 7,000 of which vest at the rate of
     3,500 per annum, 12,000 of which vest at the rate of 2,000 per annum and
     14,000 of which vest at the rate of 2,000 per annum; Mr. Ballard, 7,000
     shares ($74,813), which vest at the rate of 1,000 per annum; Mr. Chadwick,
     34,000 shares ($363,375) of which 12,000 vest at the rate of 2,000 per
     annum, 14,000 of which vest at the rate of 2,000 per annum and 8,000 of
     which vest at the rate of 1,000 per annum.  Each of the named executive
     officers are entitled to receive all dividends and other distributions paid
     with respect to those shares of  restricted stock held by such executive
     officers. 
     
(4)  Amounts in this column represent options to acquire shares of Common Stock.
     The Company does not have SARs.

(5)  The Company does not maintain any long-term incentive plans.

                                       10
<PAGE>

(6)  Amounts in this column for 1998 include premiums paid for group term life
     insurance and contributions to various Company benefit plans, which are as
     follows:   

<TABLE>
<CAPTION>
                                                       COMPANY CONTRIBUTIONS
                                                       ---------------------
                               GROUP        ENSCO       PROFIT
                             TERM LIFE     SAVINGS      SHARING
                             INSURANCE      PLAN         PLAN         SERP         TOTAL
                             ---------     -------      -------      -------      -------
<S>                          <C>           <C>          <C>          <C>          <C>
Carl F. Thorne                $7,470       $5,600       $16,000      $52,583      $81,653
Richard A. Wilson              7,259        5,600        16,000       20,107       48,966
C. Christopher Gaut              755        5,600        16,000        7,398       29,753
Marshall Ballard               3,240        5,600        16,000        8,039       32,879
William S. Chadwick, Jr.       1,958        5,600        16,000        4,664       28,222
</TABLE>

     The following table sets forth information regarding aggregated option 
exercises in 1998, the number of unexercised options segregated by those that 
were exercisable and those that were unexercisable at December 31, 1998, and 
the value of the in-the-money options segregated by those that were 
exercisable and those that were unexercisable at December 31, 1998.

<TABLE>
                                     AGGREGATED OPTION EXERCISES IN LAST FISCAL YEAR
                                            AND FISCAL YEAR-END OPTION VALUES
<CAPTION>
                                                          NUMBER OF UNEXERCISED OPTIONS  VALUE OF UNEXERCISED IN-THE-MONEY 
                              SHARES                          AT DECEMBER 31, 1998       OPTIONS AT DECEMBER 31, 1998($) 
                            ACQUIRED ON      VALUE        -----------------------------  ---------------------------------
                            EXERCISE (#)   REALIZED ($)    EXERCISABLE    UNEXERCISABLE    EXERCISABLE     UNEXERCISABLE 
                            ------------   ------------    -----------    -------------    -----------     -------------
<S>                         <C>            <C>            <C>             <C>            <C>               <C>
Carl F. Thorne                   N/A             N/A         100,000         200,000          90,625           90,625
Richard A. Wilson             12,500          96,094          71,000         165,000          39,938           27,187
Christopher Gaut              43,411         333,125          60,873         125,500          45,761           22,656
Marshall  Ballard                N/A             N/A          49,500          85,000          45,813           18,125
William S. Chadwick, Jr.      13,000          95,875          80,500          87,500         106,219           22,656
</TABLE>

- --------------------
N/A   - Not Applicable.

     The Company does not maintain a long-term incentive plan based on 
performance goals for executive officers.  Therefore, the summary table of 
Long Term Incentive Plan Awards in Last Fiscal Year as required under the 
executive compensation disclosure rules of the Commission has not been 
included.  Also, the Company does not maintain a defined benefit or actuarial 
pension plan for any of the named executive officers.  Therefore, a table on 
Pension Plan Benefits has not been included.

EMPLOYEE RETIREMENT PLAN

     Marshall Ballard was a participant in a noncontributory defined benefit
employee retirement plan previously offered to former employees of Penrod
Drilling Company (the "Penrod Plan"), which was acquired by the Company in
August 1993. The Penrod Plan was frozen effective December 31, 1990, and was
terminated in May 1998.  Mr. Ballard received a lump sum distribution of $92,007
pursuant to the termination of this Plan. 

                                       11
<PAGE>

                            REPORT OF THE NOMINATING AND
                               COMPENSATION COMMITTEE

COMPENSATION PHILOSOPHY AND OBJECTIVES

     The philosophy of the Company's compensation program is to employ, 
retain and reward executives capable of leading the Company in achieving its 
business objectives.  These objectives include the preservation of a strong 
financial posture, improvement of the size and quality of the Company's asset 
base, and positioning the Company's assets and business segments in 
geographic and industry markets offering long-term growth in profitability 
relative to the Company's competitors.  The accomplishment of these 
objectives is measured against conditions characterizing the industry within 
which the Company operates. 

EXECUTIVE OFFICER COMPENSATION

     The Company's executive officer compensation program is comprised of 
base salary, annual cash incentive compensation and long-term incentive 
compensation in the form of stock options and restricted stock.  
Additionally, executive officers may participate, on the same basis as other 
employees, in the employer matching and profit sharing provisions of the 
Company's defined contribution retirement plans which allow all employees to 
save for their retirement on a tax deferred basis.  During 1998, the maximum 
total Company matching contribution available to officers and other employees 
was 4.5% of salary, and a profit sharing contribution of 10% of eligible 
compensation was distributed.

     Base salary levels for the Company's executive officers are set relative 
to the Company's competitors and reflect the Committee's assessment of the 
executive's contribution in connection with financial and stock price 
performance and the achievement of specified business objectives.  During 
1996, the Company implemented the Key Employees' Incentive Compensation Plan 
(the "Incentive Compensation Plan"), pursuant to which key employees may 
receive both a cash bonus upon the achievement of predetermined performance 
goals, as well as additional discretionary awards as determined by the 
Committee.  The purpose of the Incentive Compensation Plan is to link the 
cash compensation of the Company's management directly to financial 
performance and certain other goals and objectives related to enhancement of 
stockholder value, and to provide a layer of variable cash compensation which 
enables the Company to be strongly competitive in attracting and retaining 
talented personnel during periods of high demand without creating an unduly 
high fixed cost overhead structure which could be burdensome during periods 
of weak demand.  Among the performance measurement criteria utilized under 
the Incentive Compensation Plan are stock price appreciation, return on 
capital employed, operating margins and general and administrative expense 
levels relative to the Company's competitors, and safety.  In accordance with 
the terms of the Incentive Compensation Plan, the Company paid cash bonuses 
to executive officers and other key management personnel in 1999, relative to 
1998 performance.  Bonuses earned under the Incentive Compensation Plan vest 
over three years, contingent upon continued employment with the Company.   
Based upon an analysis, conducted with the participation of an independent 
consultant, of data collected for comparable positions with the Company's 
competitors, the Committee believes that its executive officers' total cash 
compensation in 1998, which included discretionary as well as formula 
generated bonus payments in recogntion of the Company's record results, was 
generally near the median of that paid by the Company's competitors.  The 
competitive peer group utilized in this analysis consisted of seven publicly 
traded oil and gas drilling companies and one publicly traded marine 
transportation service company which, in the opinion of the Committee, 
comprise the Company's closest and most direct competitors.

     An additional longstanding objective of the Committee has been to reward 
executive officers with equity compensation, in keeping with the Company's 
overall compensation philosophy of placing equity in the hands of its 
employees in an effort to further instill stockholder considerations and 
values in the actions of all employees and executive officers.  Both stock 
options and grants of restricted stock have historically been used to reward 
and provide incentives to executive officers and to retain them through the 
potential of capital gains and equity build up.  Because such awards vest 
over a number of years and are therefore long-term in nature, no equity 
awards were made to executive officers during 1998.  The Committee will 
continue to review, on an annual basis, the equity participation awards 
outstanding to the executive officers of the Company, and will consider 
additional awards 

                                       12
<PAGE>

from time to time, based upon the philosophy stated above, the financial 
performance of the Company, and the Committee's assessment of each 
executive's ability to influence the Company's long-term growth and 
profitability.  Because the value of stock options and restricted stock 
should, over time, bear a direct relationship to the Company's stock price, 
the Committee believes the award of options and grants represents an 
effective incentive to create value for the stockholders. 

CHIEF EXECUTIVE OFFICER COMPENSATION

     The Chief Executive Officer's ("CEO") salary is reviewed once annually, 
consistent with the Company's salary administration policy for all shore 
based employees.  Adjustments are considered by the Committee based upon the 
Company's financial and stock price performance, its progress in achieving 
specified business objectives, and with regard to the salaries paid to chief 
executive officers of the Company's competitors.  Effective July 1, 1998, 
based upon the Committee's subjective assessment of the foregoing factors, 
the CEO's salary was increased from $475,000 to $500,000.  

     In accordance with the terms of the Incentive Compensation Plan, the CEO 
was awarded an incentive bonus of $362,268 in 1999 relative to 1998 
performance. An amount of $162,268 of this bonus was determined solely by 
reference to the pre-established formula under the Incentive Compensation 
Plan, and the discretionary portion of this bonus was based upon the 
Committee's assessment of the CEO's contribution in connection with the 
Company's financial performance in achieving a record year during 1998 and 
the achievement of other performance objectives, and with regard to the total 
compensation paid to chief executive officers of the Company's competitors. 
The performance objectives established for the CEO under the Incentive 
Compensation Plan include stock price appreciation, return on capital 
employed, margins and general and administrative expense levels relative to 
competitors and the Company's safety record.  All bonuses awarded vest over 
three years.

     No equity awards were granted to the CEO during 1998.  

     Section 162(m) of the Internal Revenue Code generally disallows a tax 
deduction to public companies for compensation over $1 million paid to each 
of the Company's chief executive officer and the four other most highly 
compensated officers, unless such compensation meets certain specific 
requirements.  The compensation programs for the Company are designed 
generally to preserve the tax deductibility of compensation paid to its 
executive officers.  The Committee will, however, take into consideration the 
various other factors described in this report, together with Section 162(m) 
considerations, in making executive compensation decisions, and could, in 
certain circumstances, pay compensation that is not fully tax deductible, if 
the Committee believes such payments are in the Company's best interest.

Nominating and Compensation Committee


Morton H. Meyerson, Chairman
Orville D. Gaither 
Thomas L. Kelly II

March 11, 1999

                                       13
<PAGE>

            COMPENSATION COMMITTEE INTERLOCKS AND INSIDER PARTICIPATION

     Mr. Thorne, President and Chief Executive Officer of the Company, has
served as a director and Chairman of the Compensation Committee of Crescent
Operating, Inc. since June 12, 1997.  Mr. Haddock, a director of the Company,
has served as President, Chief Executive Officer and director of Crescent
Operating, Inc. since April 1997.

                                 PERFORMANCE GRAPH 
                                          
     The chart below presents a comparison of the five year cumulative total 
return, assuming $100 invested on December 31, 1993 and the reinvestment of 
dividends, if any, for the Common Stock, the Standard & Poor's 500 Stock 
Price Index and the Dow Jones Oil Drilling Index.*

                COMPARISON OF FIVE YEAR CUMULATIVE TOTAL RETURN
                        ENSCO INTERNATIONAL INCORPORATED

                                       
                                    [GRAPH]

<TABLE>
<CAPTION>
                                               December 31,
                          ------------------------------------------------------
                          1993      1994      1995      1996      1997      1998
                          ----      ----      ----      ----      ----      ----
<S>                       <C>       <C>       <C>       <C>       <C>       <C>
ENSCO International 
  Incorporated            $100      $ 92      $170      $359      $497      $160
S&P 500-Registered 
  Trademark- Index         100       101       139       171       229       294
Dow Jones Oil 
  Drilling Index*          100        85       147       304       409       169
</TABLE>


*    The Dow Jones Oil Drilling Index is comprised of the following companies:
Global Marine, Inc., Rowan Companies, Inc., Helmerich & Payne, Inc., Nabors
Industries, Inc., ENSCO International Incorporated and Parker Drilling Company.

                                       14
<PAGE>

                                  PROPOSAL 2
                                       
                     APPOINTMENT OF INDEPENDENT ACCOUNTANTS

Upon the recommendation of the Audit Committee, the Board of Directors has 
approved the appointment of PricewaterhouseCoopers LLP as the Company's 
independent accountants for the year ending December 31, 1999.

     Representatives of PricewaterhouseCoopers LLP will attend the Annual 
Meeting and will be provided with the opportunity to make a statement if they 
so desire and to respond to appropriate questions.

 THE BOARD OF DIRECTORS RECOMMENDS A VOTE "FOR" APPROVAL OF THE APPOINTMENT OF
             PRICEWATERHOUSECOOPERS LLP AS INDEPENDENT ACCOUNTANTS.

GENERAL AND OTHER MATTERS

     The Company believes that Proposals 1 and 2 are the only matters that 
will be brought before the Annual Meeting.  However, if other matters are 
properly presented at the Annual Meeting, it is intended that the persons 
named in the accompanying Proxy will vote in accordance with their best 
judgment on such matters.
                                       
             SECTION 16(a) BENEFICIAL OWNERSHIP REPORTING COMPLIANCE

     Section 16(a) of the Exchange Act requires the Company's directors and 
executive officers, and persons who own more than 10% of a registered class 
of the Company's equity securities, to file with the Commission initial 
reports of ownership and reports of changes in ownership of Common Stock and 
other equity securities of the Company.  Executive officers, directors and 
greater than 10% stockholders are required by Commission regulations to 
furnish the Company with copies of all Section 16(a) forms they file.

     To the Company's knowledge, based solely upon review of the copies of 
such reports furnished to the Company during the year ended December 31, 
1998, no director, officer or beneficial holder of more than 10% of any class 
of equity securities of the Company failed to file on a timely basis reports 
required by Section 16(a) of the Exchange Act during the most recent fiscal 
year.
                                       
                  INFORMATION CONCERNING STOCKHOLDER PROPOSALS

     A holder of the Company's securities intending to present a proposal at 
the 2000 Annual Meeting must deliver such proposal, in writing, to the 
Company's principal executive offices no later than November 26, 1999 for 
inclusion in the proxy statement related to that meeting.  The proposal 
should be delivered to the Company by Certified Mail-Return Receipt 
Requested.  A holder of the Company's securities whose proposal is not 
included in the proxy statement related to the 2000 Annual Meeting, but who 
still intends to submit a proposal at that meeting is required to deliver 
such proposal, in writing, to the secretary of the Company at the Company's 
principal executive offices, and to provide certain other information not 
less than fifty (50) days, nor more than seventy-five (75) days, prior to the 
meeting, in accordance with the Bylaws. Any such proposal must also comply 
with the other provisions contained in the Company's Bylaws relating to 
shareholder proposals.

     A copy of the Company's Annual Report to Stockholders for the year ended 
December 31, 1998 has been, or is being, mailed to Stockholders with this 
Proxy Statement.  The Annual Report to Stockholders does not constitute a 
part of the proxy soliciting material.

     Whether or not you intend to be present at the Annual Meeting, you are 
urged to return your Proxy promptly.  If you are present at the Annual 
Meeting and wish to vote your stock in person, your Proxy shall, at your 
request, be returned to you at the Annual Meeting.

                                       15


<PAGE>
                                       
                                     PROXY
                        ENSCO INTERNATIONAL INCORPORATED

                BOARD OF DIRECTORS PROXY FOR THE ANNUAL MEETING
              OF STOCKHOLDERS AT 10:00 A.M., TUESDAY, MAY 18, 1999
                         FAIRMONT HOTEL, 1717 N. AKARD
                             DALLAS, TEXAS 75201

     The undersigned stockholder of ENSCO International Incorporated (the 
"Company") hereby appoints Carl F. Thorne and C. Christopher Gaut or either 
of them, each with full power of substitution, to vote the shares of the 
undersigned at the above-stated Annual Meeting and any adjournment(s) thereof:

     THIS PROXY IS SOLICITED ON BEHALF OF THE BOARD OF DIRECTORS AND WILL BE 
VOTED IN ACCORDANCE WITH THE SPECIFICATIONS MADE HEREIN. IF A CHOICE IS NOT 
INDICATED WITH RESPECT TO ITEMS (1) AND (2), THIS PROXY WILL BE VOTED "FOR" 
SUCH ITEMS. THE PROXIES WILL USE THEIR DISCRETION WITH RESPECT TO ANY MATTER 
REFERRED TO IN ITEM (3). THIS PROXY IS REVOCABLE AT ANY TIME BEFORE IT IS 
EXERCISED.
                                       
                       (PLEASE SIGN ON THE REVERSE SIDE)

<PAGE>
                                       
                        PLEASE DATE, SIGN AND MAIL YOUR
                      PROXY CARD BACK AS SOON AS POSSIBLE!

                        ANNUAL MEETING OF STOCKHOLDERS
                       ENSCO INTERNATIONAL INCORPORATED

                                 MAY 18, 1999



               - Please Detach and Mail in the Envelope Provided -

                          __
/X/  PLEASE MARK YOUR     |                                                  |
     VOTES AS IN THIS                                                        ---
     EXAMPLE.

<TABLE>
<CAPTION>
                       FOR ALL NOMINEES
                    LISTED AT RIGHT (EXCEPT
                       AS MARKED TO THE
                        CONTRARY BELOW)         WITHHOLD
<S>                 <C>                         <C>          <C>
1.  Election of              / /                  / /        NOMINEES:  Craig I. Fields
    Class II                                                            Morton H. Meyerson
    Directors:                                                          Richard A. Wilson

(INSTRUCTION: To vote against any individual
nominee, strike a line through the nominee's name
in the list at right.)

                                        FOR     AGAINST    ABSTAIN
2.  Approval of the appointment of      / /       / /        / /
    PricewaterhouseCoopers LLP as 
    independent accountants for 1999.


3.  On any other business that may properly come before the Annual Meeting,
    in the discretion of the proxies, hereby revoking any proxy or proxies
    heretofore given by the undersigned.

PLEASE SIGN, DATE AND MAIL TODAY.

Change of Address/Comments

- ---------------------------------------

- ---------------------------------------

- ---------------------------------------



Signature of Stockholder(s)                                                                         Date:                     , 1999
                           ---------------------------------   ---------------------------------        ----------------------
                                                                 (SIGNATURE IF HELD JOINTLY)

Note:  Please sign exactly as your name appears hereon. Joint owners should each sign. When signing as attorney, executor, 
       administrator, trustee or guardian, please give full title as such.
</TABLE>



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