NOBLE DRILLING CORP
DEF 14A, 1999-03-22
DRILLING OIL & GAS WELLS
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<PAGE>   1
                            SCHEDULE 14A INFORMATION

Proxy Statement Pursuant to Section 14(a) of the Securities Exchange Act of 1934
                                (Amendment No. )

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

                           NOBLE DRILLING CORPORATION
                (Name of Registrant as Specified In Its Charter)

                           NOBLE DRILLING CORPORATION
                   (Name of Person(s) Filing Proxy Statement)


Payment of Filing Fee (Check the appropriate box):

[X]      No fee required.

[ ]      Fee computed on table below per Exchange Act Rules 14a-6(i)(1) 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 price or other underlying value of transaction
                  computed pursuant to Exchange Act Rule 0-11:1
                  .............................................................
         4)       Proposed maximum aggregate value of transaction:
                  .............................................................
         5)       Total fee paid:
                  .............................................................
(1) Set forth the amount on which the filing fee is calculated and state how it
    was determined.

[ ]      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>   2



                                  [NOBLE LOGO]

                           NOBLE DRILLING CORPORATION
                        10370 RICHMOND AVENUE, SUITE 400
                              HOUSTON, TEXAS 77042

                    NOTICE OF ANNUAL MEETING OF STOCKHOLDERS

                          TO BE HELD ON APRIL 22, 1999


To the Stockholders of
  Noble Drilling Corporation:

      The annual meeting of stockholders of Noble Drilling Corporation, a
Delaware corporation (the "Company"), will be held on Thursday, April 22, 1999,
at 10:00 a.m., local time, at the Luxury Collection Hotel, the former Ritz
Carlton Hotel, 1919 Briar Oaks Lane, Houston, Texas, for the following purposes:

            1.    To elect three directors to the class of directors whose 
                  three-year term will expire in 2002;

            2.    To consider and vote upon a proposal to increase by 5,000,000
                  the number of shares of Common Stock available under the
                  Company's 1991 Stock Option and Restricted Stock Plan; and

            3.    To transact such other business as may properly come before 
                  the meeting or any adjournment thereof.

      The Board of Directors has fixed the close of business on March 8, 1999 as
the record date for the determination of stockholders entitled to notice of and
to vote at the annual meeting or any adjournment thereof. Only holders of record
of Common Stock at the close of business on the record date are entitled to
notice of and to vote at the meeting. A complete list of such stockholders will
be available for examination at the offices of the Company in Houston, Texas
during normal business hours for a period of 10 days prior to the meeting.

      A record of the Company's activities during 1998 and financial statements
for the fiscal year ended December 31, 1998 are contained in the accompanying
1998 Annual Report. The Annual Report does not form any part of the material for
solicitation of proxies.

      All stockholders are cordially invited to attend the meeting. Stockholders
are urged, whether or not they plan to attend the meeting, to sign, date and
mail the enclosed proxy or voting instruction card in the postage-paid envelope
provided. If a stockholder who has returned a proxy attends the meeting in
person, such stockholder may revoke the proxy and vote in person on all matters
submitted at the meeting.


                                         By Order of the Board of Directors

                                                Julie J. Robertson
                                                      Secretary


Houston, Texas
March 22, 1999


<PAGE>   3




                                  [NOBLE LOGO]


                           NOBLE DRILLING CORPORATION
                        10370 RICHMOND AVENUE, SUITE 400
                              HOUSTON, TEXAS 77042

                                 PROXY STATEMENT

                       FOR ANNUAL MEETING OF STOCKHOLDERS
                          TO BE HELD ON APRIL 22, 1999

                                     GENERAL

      This proxy statement is furnished to stockholders of Noble Drilling
Corporation (the "Company") in connection with the solicitation by the Board of
Directors of the Company of proxies for use at the annual meeting of
stockholders to be held at the time and place and for the purposes set forth in
the accompanying notice. The approximate date of mailing of this proxy statement
and the accompanying proxy or voting instruction card is March 22, 1999.

PROXY CARDS AND VOTING INSTRUCTION CARDS

      If a proxy card is enclosed, it serves to appoint proxies for record
holders of common stock, par value $.10 per share ("Common Stock"), of the
Company. Shares represented by a proxy in such form, duly executed and returned
to the Company and not revoked, will be voted at the meeting in accordance with
the directions given. If no direction is made, the proxy will be voted for
election of the directors named in the proxy and for the proposal to increase
the number of shares of Common Stock available under the Company's 1991 Stock
Option and Restricted Stock Plan (the "Option Plan"). Any stockholder giving a
proxy may revoke it at any time before it is voted by communicating such
revocation in writing to the Secretary of the Company or by executing and
delivering a later-dated proxy.

      If a voting instruction card is enclosed, it serves as a voting
instruction to the trustee of the Noble Drilling Corporation Thrift Plan, as
amended (the "Thrift Plan"), from the plan participant. The trustee under the
Thrift Plan will vote the shares of Common Stock credited to Thrift Plan
participants' accounts in accordance with such participants' instructions. If no
such voting instructions are received from a participant, then, according to the
terms of the Thrift Plan, the trustee under the Thrift Plan will vote the shares
in such participant's account in its absolute discretion.

VOTING PROCEDURES AND TABULATION

      The Company will appoint one or more inspectors of election to act at the
meeting and to make a written report thereof. Prior to the meeting, the
inspectors will sign an oath to perform their duties in an impartial manner and
according to the best of their ability. The inspectors will ascertain the number
of shares outstanding and the voting power of each, determine the shares
represented at the meeting and the validity of proxies and ballots, count all
votes and ballots, and perform certain other duties as required by law.

      With regard to the election of directors, votes may be cast in favor of or
withheld from each nominee. Votes that are withheld will be excluded entirely
from the vote and will have no effect. Abstentions may be specified with respect
to the proposal to approve and ratify the amendment to the Option Plan, and will
be counted as present for purposes of determining the existence of a quorum
regarding such item of business. Abstentions with respect to this proposal will
have the effect of a negative vote because it requires the affirmative vote of a
majority of shares of Common Stock present in person or represented by proxy at
the meeting and entitled to vote thereon. Under the rules of the New York Stock
Exchange, brokers who hold shares in street name have the authority to vote on
certain "routine" items when they have not received instructions from beneficial
owners. Brokers will have discretionary authority to vote on the scheduled items
of business. Under applicable Delaware law, a broker non-vote (or other limited
proxy) will have no effect on the outcome of the election of directors or the
proposal to approve and ratify the amendment to the Option Plan.


<PAGE>   4



                                VOTING SECURITIES

      The only voting security of the Company outstanding is its Common Stock.
Only holders of record of Common Stock at the close of business on March 8,
1999, the record date for the meeting, are entitled to notice of and to vote at
the meeting. On the record date for the meeting, there were 131,142,998 shares
of Common Stock outstanding and entitled to be voted at the meeting. A majority
of such shares, present in person or represented by proxy, is necessary to
constitute a quorum. Each share of Common Stock is entitled to one vote.


                 SECURITY OWNERSHIP OF CERTAIN BENEFICIAL OWNERS

      The following table sets forth as of December 31, 1998 information with
respect to the only persons who were known to the Company to be the beneficial
owners of more than five percent of the outstanding shares of Common Stock.



<TABLE>
<CAPTION>
                 Name and Address of                                         Common Stock
                   Beneficial Owner                                       Beneficially Owned
                 -------------------                                      ------------------
                                                                   Number                Percent of
                                                                  of Shares                 Class
                                                                  ----------             ----------
<S>                                                               <C>                    <C>  
The Equitable Companies Incorporated..................            21,909,980(1)             16.7%
1290 Avenue of the Americas
New York, New York 10104
</TABLE>

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

(1)       Amount in table reflects number of shares beneficially owned as of
          December 31, 1998. According to Schedule 13G (Amendment No. 3), dated
          February 10, 1999, filed with the Securities and Exchange Commission
          ("SEC") by The Equitable Companies Incorporated (the "Equitable
          Companies") jointly with AXA Conseil Vie Assurance Mutuelle, AXA
          Assurances I.A.R.D. Mutuelle, AXA Assurances Vie Mutuelle, and AXA
          Courtage Assurance Mutuelle (collectively, the "Mutuelles AXA") and
          AXA, the amount beneficially owned as of December 31, 1998 consists of
          (i) 2,403,700 shares beneficially owned by The Equitable Life
          Assurance Society of the United States ("Equitable"), with respect to
          which it has sole investment power and with respect to 2,354,700
          shares of which it has sole voting power, (ii) 19,472,480 shares
          beneficially owned by Alliance Capital Management L.P. ("Alliance"),
          with respect to which it has sole investment power and with respect to
          8,521,120 shares of which it has sole voting power, (iii) 15,700
          shares beneficially owned by Donaldson, Lufkin & Jenrette Securities
          Corporation ("DLJ"), with respect to 400 shares of which it has sole
          investment power and with respect to 15,300 of which it has shared
          investment power, (iv) 17,300 shares beneficially owned by Wood,
          Struthers & Winthrop Management Corporation ("WSW"), with respect to
          12,000 shares of which it has sole investment power and with respect
          to 5,300 shares of which it has sole voting power, and (v) 800 shares
          beneficially owned by Sun Life and Provincial Holdings PLC ("Sun
          Life"), with respect to which it has sole investment and sole voting
          power.



                                        2


<PAGE>   5



                              ELECTION OF DIRECTORS

    The Certificate of Incorporation and Bylaws of the Company provide for three
classes of directors, with one-third of the directors constituting the Board
being elected each year to serve a three-year term. Pursuant to the Company's
Bylaws, the number of directors has been established by resolution of the Board
at nine.

    The Board of Directors has nominated Lawrence J. Chazen, William J. Dore and
William A. Sears from the class of directors whose term expires at the 1999
annual meeting for re-election as directors of the Company to serve three-year
terms expiring in 2002.

    The directors nominated for election this year will be elected by a
plurality of the shares of Common Stock present in person or represented by
proxy at the meeting and entitled to vote. All duly submitted and unrevoked
proxies in the form enclosed will be voted for the nominees selected by the
Board of Directors, except where authorization so to vote is withheld. THE BOARD
RECOMMENDS THAT STOCKHOLDERS VOTE FOR THE ELECTION OF ITS NOMINEES FOR DIRECTOR.

    Information with respect to the directors nominated for election this year,
and the directors whose terms do not expire at the 1999 annual meeting, is
presented below.

<TABLE>
<CAPTION>
                                           NOMINEES FOR DIRECTORS
<S>                                    <C>
LAWRENCE J. CHAZEN,
age 58, director since 1994            Mr. Chazen has served since 1977 as Chief Executive Officer of Lawrence J.
                                       Chazen, Inc., a California registered investment adviser engaged in providing
                                       financial advisory services.

WILLIAM J. DORE,
age 56, director since 1997            Mr. Dore has served since 1973 as Chairman, President and Chief Executive Officer
                                       of Global Industries, Ltd., a company engaged in the business of offshore
                                       construction and support services.

WILLIAM A. SEARS,
age 64, director since 1998            Mr. Sears retired from his position as Director of Operations for British Petroleum
                                       Exploration ("BPX") in 1997, after serving with BPX in various positions since
                                       1983.

                                          CLASS WHOSE TERM EXPIRES IN 2001

MICHAEL A. CAWLEY,
age 51, director since 1985            Mr. Cawley has served as President and Chief Executive Officer of The Samuel
                                       Roberts Noble Foundation, Inc. (the "Foundation") since February 1, 1992, after
                                       serving as Executive Vice President of the Foundation since January 1, 1991.  For
                                       more than five years prior to 1991, Mr. Cawley was the President of Thompson &
                                       Cawley, a professional corporation, attorneys at law; and Mr. Cawley currently
                                       serves as of counsel to the law firm of Thompson, Cawley, Veazey & Burns, a
                                       professional corporation.  Mr. Cawley has served as a trustee of the Foundation
                                       since 1988 and is also a director of Noble Affiliates, Inc. and Panhandle Royalty
                                       Company.

TOMMY C. CRAIGHEAD,
age 70, director since 1988            Mr. Craighead is the President and owner of T. C. Craighead & Company (which
                                       is the general partner of The Joy Partners, Ltd.) and Astro Oil, Inc., all based in
                                       Ardmore, Oklahoma.  He is also Vice-President of Tom-Sam, Inc.  He has been an
                                       oil and gas lease broker and independent operator since 1962.
</TABLE>


                                        3


<PAGE>   6



<TABLE>
<S>                                    <C>
JAMES L. FISHEL,
age 67, director since 1989            Mr. Fishel retired as Vice President and Manager of Corporate Credit Operations
                                       of General Electric Capital Corporation ("GECC") in 1994, after serving with
                                       GECC in various positions since 1974.  He is also a director of American Health
                                       Properties, Inc., which is a real estate investment company.

                                          CLASS WHOSE TERM EXPIRES IN 2000

ROBERT D. CAMPBELL
age 48, director since 1999            Mr. Campbell has served as President of the Company since January 1, 1999 and as
                                       a Director since February 4, 1999.  Prior to January 1, 1999, Mr. Campbell practiced
                                       corporate and securities law as a senior shareholder with the law firm of Thompson
                                       & Knight, P.C. and served as general counsel to the Company for more than five
                                       years.

JAMES C. DAY,
age 55, director since 1983            Mr. Day has served as Chairman of the Board since October 22, 1992 and as Chief
                                       Executive Officer of the Company since January 1, 1984, and he served as President
                                       from January 1, 1984 to January 1, 1999.  From January 1983 until his election as
                                       President and Chief Executive Officer, Mr. Day served as Vice President of the
                                       Company.  Mr. Day is also a director of Global Industries, Ltd. and Noble Affiliates,
                                       Inc.

MARC E. LELAND,
age 60, director since 1994            Mr. Leland has served since 1984 as President of Marc E. Leland & Associates,
                                       Inc., a company engaged in the business of providing financial advisory services.
                                       Mr. Leland is also a director of Chartwell Leisure Inc.
</TABLE>


             ADDITIONAL INFORMATION REGARDING THE BOARD OF DIRECTORS

BOARD MEETINGS AND COMMITTEES

    During 1998 the Board of Directors held six meetings. The Company has
standing audit, compensation, finance and nominating committees of the Board of
Directors. The current members of the committees, number of meetings held by
each committee in 1998, and a brief description of the functions performed by
each committee are set forth below:

          Audit Committee (four meetings). Lawrence J. Chazen, Chairman; James
    L. Fishel; and William A. Sears. The primary responsibilities of the audit
    committee are to review with the Company's auditors the scope of the audit
    procedures to be applied in conducting the annual audit and the results of
    the annual audit. In addition, the audit committee has responsibility to
    provide oversight review to the management of the Company and its
    subsidiaries responsible for the periodic review of the Company's
    environmental policy statement and procedures and internal controls
    regarding compliance with applicable environmental laws and regulations and
    the establishment of a program for periodic compliance audits.

          Compensation Committee (four meetings).  Tommy C. Craighead, Chairman;
    Michael A. Cawley; William J. Dore; and Marc E. Leland. The primary
    responsibilities of the compensation committee are to review and set the
    compensation levels of the officers of the Company, including those officers
    who are also directors, evaluate the performance of management, consider
    management succession and related matters, administer the annual
    compensation plans of the Company and administer the long-term incentive
    compensation plans of the Company.



                                        4


<PAGE>   7



          Finance Committee (one meeting). James L. Fishel, Chairman; Michael A.
    Cawley; and James C. Day. The primary responsibilities of the finance
    committee, which was established in October 1998, are to review and make
    recommendations to the Board of Directors with regard to the financial
    affairs and policies of the Corporation, including capital requirements and
    structure, share repurchase programs, dividend policy and long-range
    financial strategic planning.

          Nominating Committee (one meeting). Michael A. Cawley, Chairman; Tommy
    C. Craighead; and James C. Day. The primary responsibility of the nominating
    committee is to select and recommend nominees for director of the Company.
    The nominating committee will consider nominees recommended by stockholders
    entitled to vote for the election of directors, provided that such
    recommendations are made in accordance with the Bylaws of the Company.
    Generally, the Bylaws provide that a stockholder must deliver written notice
    to the Secretary of the Company not later than 90 days prior to the annual
    meeting naming such stockholder's nominee(s) for director and specifying
    certain information concerning such stockholder and nominee(s). Accordingly,
    stockholder nominee(s) for director to be presented at the 2000 annual
    meeting of stockholders must be received by the Company no later than
    January 21, 2000.

    Compensation Committee Interlocks and Insider Participation. The current
members of the compensation committee identified above were the only persons who
served on such committee during 1998. Mr. Day serves as an executive officer of
certain wholly owned subsidiaries of the Company, and in some instances, one or
more directors of these subsidiaries is also an executive officer of the
Company. However, Mr. Day's compensation is set solely by the compensation
committee of the Board of Directors of the Company, and he receives no
additional compensation for performing duties as an executive officer of these
subsidiaries. Neither Mr. Day nor any other officer or employee of the Company
or its subsidiaries is a member of the Company's compensation committee.

COMPENSATION OF DIRECTORS

    Annual Retainer and Other Fees and Expenses. Non-employee directors are paid
an annual retainer of $25,000, of which $5,000 is paid in Common Stock pursuant
to the Equity Compensation Plan for Non-Employee Directors (the "Directors'
Plan"). Under the Directors' Plan, non-employee directors may elect to receive
the balance in Common Stock or cash. Non-employee directors receive a Board
meeting fee of $1,000 and a committee meeting fee of $500. The chairman of a
standing Board committee receives an additional $500 per committee meeting. A
director who is an officer of the Company receives a fee of $100 for each Board
meeting attended. The Company also reimburses directors for travel, lodging and
related expenses they may incur in attending Board and committee meetings.

    Non-Employee Director Stock Options. Under the 1992 Nonqualified Stock
Option Plan for Non-Employee Directors (the "1992 Option Plan"), which was
approved and ratified by stockholders at the 1993 annual meeting, non-employee
directors receive a one-time grant of an option to purchase 10,000 shares of
Common Stock. Thereafter, on the next business day after each annual meeting of
stockholders of the Company, such directors receive an annual grant of an option
to purchase 3,500 shares of Common Stock. The options are granted at fair market
value on the grant date and are exercisable from time to time over a period
commencing one year from the grant date and ending on the expiration of 10 years
from the grant date, unless terminated sooner as described in the 1992 Option
Plan.

EMPLOYMENT AGREEMENTS

    James C. Day, Robert D. Campbell, Byron L. Welliver and Julie J. Robertson,
in their capacities as (i) Chairman and Chief Executive Officer, (ii) President,
(iii) Senior Vice President - Finance, Treasurer and Controller and (iv)
Corporate Secretary and Vice President - Administration, respectively, have each
executed employment agreements with the Company. These employment agreements
become effective upon a change of control of the Company (within the meaning set
forth in the agreements) or a termination of employment in connection with or in
anticipation of a change of control, and remain effective for three years
thereafter.

    The agreements provide that if the officer's employment is terminated within
three years after a change of control or prior to but in anticipation of a
change of control, either (1) by the Company for reasons other than death,
disability or "cause" (as defined in the agreement) or (2) by the officer for
"good reason" (which term includes a diminution of responsibilities or
compensation, or a determination by the officer to leave during the 30-day
period immediately following the first anniversary of the change of control),
the officer will receive: (a) any unpaid portion of his current salary and
prorated portion of his highest bonus paid either in the last three years before
the change of control or for the last completed fiscal year after the change of
control (the "Highest Bonus"); (b) a lump sum payment equal to three times

                                        5


<PAGE>   8



the sum of his annual base salary (based on the highest monthly salary paid in
the 12 months prior to the change of control) and his Highest Bonus; (c)
benefits to him and his family at least equal to those which would have been
provided had the employment not been terminated for a three-year period; (d) any
compensation previously deferred by the officer (together with any accrued
interest or earnings thereon) and any accrued vacation pay; and (e) a lump sum
amount equal to the excess of (i) the actuarial equivalent of the benefit under
the qualified defined benefit retirement plan of the Company and its affiliated
companies in which the officer is eligible to participate had the officer's
employment continued for three years after termination over (ii) the actuarial
equivalent of the officer's actual benefit under such plans. The agreements also
require the Company to make an additional payment in an amount such that after
the payment of all income and excise taxes, the officer will be in the same
after-tax position as if no excise tax under Section 4999 of the Internal
Revenue Code (the so-called Parachute Payment excise tax), if any, had been
imposed.

                        SECURITY OWNERSHIP OF MANAGEMENT

    The following table sets forth as of January 31, 1999 the beneficial
ownership of Common Stock by each director of the Company, each named executive
officer listed in the Summary Compensation Table appearing on page 10 of this
proxy statement, and all directors and executive officers as a group.

<TABLE>
<CAPTION>
                                                                    COMMON STOCK
                                                                 BENEFICIALLY OWNED (1)       
                                                             ----------------------------
                                                              NUMBER           PERCENT OF
NAME                                                         OF SHARES          CLASS (2)   
- - ----                                                         ---------         ----------
<S>                                                          <C>               <C>
Directors
Robert D. Campbell.....................................         15,000                 --
Michael A. Cawley......................................      2,204,233 (3)(4)         1.7%
Lawrence J. Chazen.....................................         27,639 (4)             --
Tommy C. Craighead.....................................         82,656 (4)             --
James C. Day...........................................        670,225 (4)            0.5%
William J. Dore........................................        216,571                0.2%
James L. Fishel........................................         26,612 (4)             --
Marc E. Leland.........................................         56,733 (4)             --
William A. Sears.......................................         12,206                 --

Named Executive Officers (excluding
  any director named above) and Group
Byron L. Welliver......................................        300,346 (4)            0.2%
Julie J. Robertson.....................................        131,337 (4)            0.1%

All directors and executive
  officers as a group (11 persons).....................      3,743,558 (5)            2.9%
</TABLE>

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

(1)  Unless otherwise indicated, the beneficial owner has sole voting and
     investment power with respect to all shares listed.

(2)  The percent of class shown is less than one-tenth of one percent unless
     otherwise indicated.

(3)  Includes 2,174,639 shares held of record by the Foundation. Mr. Cawley, as
     President and Chief Executive Officer and a trustee of the Foundation, may
     be deemed to beneficially own, and have voting and investment power with
     respect to, the 2,174,639 shares held by the Foundation. As one of the 10
     members of the board of trustees of the Foundation, Mr. Cawley does not
     represent sufficient voting power on the Foundation's board of trustees to
     determine voting or investment decisions with respect to the 2,174,639
     shares. Mr. Cawley disclaims any pecuniary interest in the 2,174,639
     shares.

(4)  Includes shares attributable to shares of Common Stock not outstanding but
     subject to currently exercisable options, as follows: Mr. Cawley -- 24,000
     shares; Mr. Chazen -- 17,000 shares; Mr. Craighead -- 24,000 shares; Mr.
     Day -- 524,832 shares; Mr. Fishel -- 24,000 shares; Mr. Leland -- 17,000
     shares; Mr. Welliver -- 250,665 shares; and Ms. Robertson -- 111,466
     shares.

(5)  Includes 992,963 shares not outstanding but subject to currently
     exercisable options and 2,174,639 shares held of record by the Foundation.
     See footnotes (3) and (4) above.


                                        6


<PAGE>   9



                             EXECUTIVE COMPENSATION

      The following report of the compensation committee on executive
compensation and the information herein under "Executive
Compensation--Performance Graph" shall not be deemed to be "soliciting material"
or to be "filed" with the SEC or subject to the SEC's proxy rules, except for
the required disclosure herein, or to the liabilities of Section 18 of the
Securities Exchange Act of 1934 (the "Exchange Act"), and such information shall
not be deemed to be incorporated by reference into any filing made by the
Company under the Securities Act of 1933 or the Exchange Act.

                      REPORT OF THE COMPENSATION COMMITTEE
                            ON EXECUTIVE COMPENSATION

To the Stockholders
of Noble Drilling Corporation:

      As members of the compensation committee (the "Committee") of the Board of
Directors, it is our responsibility to review and set the compensation levels of
the Company's Chief Executive Officer ("CEO") and other executives, evaluate the
performance of management, and consider management succession and related
matters. In addition, we administer the annual and long-term incentive
compensation plans of the Company. All decisions by the Committee relating to
the compensation of executive officers are reviewed by the full Board, except
for decisions about grants or awards under the 1991 Stock Option and Restricted
Stock Plan (the "Option Plan") of the Company, which are made solely by the
Committee in accordance with the terms of the Option Plan.

      The Company has retained the services from time to time of Towers Perrin
("Towers Perrin") and William M. Mercer, Incorporated ("Mercer"), management and
compensation consulting firms, to assist the Committee in the performance of its
responsibilities. The Committee considers information with respect to the
reasonableness of compensation paid to senior officers of the Company, as well
as all employees of the Company and its subsidiaries in managerial positions.
The Committee also takes into account how compensation compares to compensation
paid by competitors in the Company's industry as well as the performance of the
Company. Members of the Committee review results of compensation surveys
provided by Towers Perrin, Mercer and others.

COMPENSATION POLICIES AND PROGRAMS

      The compensation policies of the Company, set by management and supported
by the Committee, focus on enhancing stockholder value. Specific policies are
designed to attract, motivate and retain persons of high quality who will have
the skill, training and dedication to assist the Company to achieve its
corporate goals. The executive compensation program for 1998 consisted of three
elements: base salary, annual incentive bonus, and long-term incentive through
the granting of stock options and awarding of restricted stock pursuant to the
Option Plan.

      Base Salary: Base salary for executive officers is determined principally
by competitive factors and the marketplace. The policy of the Committee is
generally to set base salary levels for positions at approximately the median
levels determined from survey information for positions deemed comparable by the
Committee.

      Annual Incentive Bonus: The compensation policy of the Company is that a
part of the annual compensation of each officer be related to and contingent
upon the performance of the Company, as well as the individual contribution of
each officer. The short-term incentive compensation plan of the Company (the
"STIP") is available to all full-time employees of the Company or its
subsidiaries in salary classifications 18 and higher who have completed one year
of service at the close of the plan year (December 31). The bonus earned by
employees with less than two years of service is prorated based on the number of
full months served. The target bonus for an employee is the base salary at year
end of such employee multiplied times the percentage factor assigned to such
employee's salary classification. Target percentage factors range from 10 to 75
percent, with a factor of 75 percent for the CEO and a maximum factor for an
executive officer other than the CEO of 55 percent.

      Annual performance goals for the Company for 1998 were weighted with 
respect to two criteria as follows: total stockholder return (defined as share
price performance compared to industry peer group) (50 percent) and achievement
of certain EVA targets (EVA is defined as net operating profits after taxes less
a capital charge) (50 percent). The

                                        7


<PAGE>   10



division goals for 1998 were weighted with respect to four criteria as follows:
EVA targets (30 percent), budgeted capital expenditures (30 percent), safety
results (20 percent) and rig maintenance (20 percent).

      Each goal weighting percentage is subject to adjustment within a range of
zero for achievement of less than 75 percent of the goal to 200 percent for
achievement of greater than 135 percent of the goal. The combined, weighted goal
achievement is then determined within a range of zero for achievement of less
than 75 percent of the goal to 200 percent for achievement of more than 135
percent of the goal. The target bonus for employees of divisions is also
adjusted to reflect the combined percentage of achievement of all assigned goals
using the ratio of 50 percent for operating region goal achievement and 50
percent for Company goal achievement. The bonus amount is then determined by
multiplying the target bonus times the applicable multiplier. Using these
percentages, the bonus received by the CEO will not exceed 150 percent of his
salary and the bonus received by any executive officer other than the CEO will
not exceed 110 percent of his salary.

      Long-term Incentive Compensation: It is also the compensation policy of
the Company to use stock options and restricted stock as a means of furnishing
longer-term incentive to officers and other employees of the Company and its
subsidiaries. Under the Option Plan, which was approved by stockholders at the
1991 annual meeting and amended with stockholder approval in 1994 and 1997, and
further amendments which will be presented to stockholders at the 1999 annual
meeting for their approval, the Company has flexibility in creating options and
awarding restricted stock.

      On January 29, 1998, the Committee awarded an aggregate of 22,000 shares
of restricted stock to a total of five employees, including three executive
officers of the Company. The shares of restricted stock are subject to
vesting/forfeiture provisions over a five-year period and continuous employment
by the awardee. The Common Stock had a fair market value at the date of award of
$28.31 per share.

      On January 29, 1998, July 23, 1998 and October 22, 1998, the Committee
granted stock options to officers of the Company. Each officer received stock
options that were based on his or her responsibilities and relative position in
the Company. All stock options in 1998 were granted with an exercise price of
fair market value at the date of grant. One-third of the stock options granted
in January and October vest annually commencing on the first anniversary of the
date of grant. One-fifth of the stock options granted in July vest annually
commencing on the first anniversary of the date of grant.

      On February 4, 1999, the Committee awarded an aggregate of 190,000 shares
of restricted stock to a total of nine employees, including three executive
officers of the Company. The shares of restricted stock are subject to
vesting/forfeiture provisions over a five-year period and continuous employment
by the awardee. The Common Stock had a fair market value at the date of award of
$13.63 per share.

1998 COMPENSATION OF CEO

      The 1998 salary of the CEO was determined by the Committee in October 1997
as a function of performance and competitive industry factors as provided by
Towers Perrin. In October 1998, the Committee, upon the recommendation of the
CEO, did not grant an increase to the CEO, based on current industry economics.

      In determining that no bonus would be paid to the CEO under the STIP, the
Committee applied the performance goals criteria and adjustment factors as
discussed above under "Annual Incentive Bonus." Upon recommendation of the CEO,
the Committee did not grant the CEO a discretionary bonus.

      On February 4, 1999, the Committee awarded the CEO 50,000 shares of
restricted stock in lieu of a bonus for 1998 and a salary increase for 1999. The
award vests one-fifth annually.

      On January 29, 1998, July 23, 1998 and October 22, 1998, the Committee
granted the CEO, pursuant to the Option Plan, options to purchase 100,000,
50,000 and 100,000 shares of Common Stock, respectively. In granting these
options, the Committee relied upon competitive data provided by Towers Perrin
and its own assessment of the Company's 1998 results of operations under the
CEO's leadership. Pursuant to the above-described policies and programs
regarding restricted stock awarded under the Option Plan, the Committee awarded
the CEO 10,000 shares of restricted stock in January 1998.


                                        8


<PAGE>   11



TAX DEDUCTIBILITY OF EXECUTIVE COMPENSATION

      Section 162(m) of the Internal Revenue Code contains provisions which
could limit the deductibility of certain compensation payments to the Company's
executive officers. The Company believes that any compensation realized in
connection with the exercise of stock options granted by the Company will
continue to be deductible as performance-based compensation. The policy of the
Company is to design its compensation programs generally to preserve the tax
deductibility of compensation paid to its executive officers. The Committee
could determine, however, taking into consideration the burdens of compliance
with Section 162(m) and other relevant facts and circumstances, to pay
compensation that is not fully deductible, if the Committee believes such
payments are in the Company's best interests.

SUMMARY

      The members of the Committee believe that linking executive compensation
to corporate performance results in a better alignment of compensation with
corporate goals and stockholder interests. As performance goals are met or
exceeded, resulting in increased value to stockholders, executive officers are
to be rewarded commensurately. The members of the Committee believe that
compensation levels during 1998 adequately reflect the compensation goals and
policies of the Company.

March 11, 1999                                  COMPENSATION COMMITTEE

                                                Tommy C. Craighead, Chairman
                                                Michael A. Cawley
                                                William J. Dore
                                                Marc E. Leland



                                        9


<PAGE>   12



      The following table sets forth certain summary information concerning the
compensation awarded to, earned by or paid to the Chief Executive Officer of the
Company and each other person who is an executive officer of the Company whose
combined salary and bonus for 1998 exceeded $100,000 (collectively, the "named
executive officers") for the years indicated.


                           SUMMARY COMPENSATION TABLE

<TABLE>
<CAPTION>
                                                                                  LONG-TERM
                                                                                 COMPENSATION
                                     ANNUAL COMPENSATION                            AWARDS
                                     --------------------------------------------------------------------
                                                                                   SECURITIES    VALUE OF
                                                              OTHER                UNDERLYING   LONG TERM
                                                             ANNUAL    RESTRICTED   OPTIONS     INCENTIVE   ALL OTHER
         NAME AND                                            COMPEN-     STOCK     (NUMBER OF      PLAN     COMPEN-
    PRINCIPAL POSITION       YEAR     SALARY       BONUS      SATION   AWARDS(1)   SHARES)(2)   PAY-OUTS     SATION
    ------------------       ----    ---------   ---------   -------   ----------  -----------  ---------   ---------
<S>                          <C>     <C>         <C>         <C>       <C>         <C>          <C>         <C>       
James C. Day,                1998    $ 525,000   $       0   $ 6,995   $  960,500      250,000  $ 760,296   $  15,654 (3)
Chairman and CEO             1997    $ 504,167   $ 393,750   $ 4,918   $        0      175,000  $ 470,459   $  16,404
                             1996    $ 425,000   $ 700,000   $ 5,476   $  500,000      100,000  $       0   $  13,023


Byron L. Welliver,           1998    $ 230,000   $       0   $ 3,539   $  302,275      120,000  $ 237,008   $  11,134 (4)
Senior Vice President--      1997    $ 217,500   $ 126,500   $ 3,181   $        0       54,000  $ 129,375   $  11,015
Finance, Treasurer and       1996    $ 191,667   $ 150,500   $ 3,488   $  137,500       40,000  $       0   $   9,883
Controller                                                         


Julie J. Robertson,          1998    $ 155,000   $       0   $     0   $  341,825      110,000  $  78,126   $   9,300 (4)
Vice President--             1997    $ 138,333   $  69,750   $     0   $        0       37,000  $  43,108   $   8,300
Administration and           1996    $ 115,833   $  81,000   $     0   $   45,800       25,000  $       0   $   6,950
Corporate Secretary                                                          
</TABLE>

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

(1)  Dollar values of awards of restricted Common Stock ("Restricted Shares")
     shown in the table for 1996 are based on the closing price of the Common
     Stock on July 24, 1996 ($13.75), the day preceding the date of the awards,
     and represent the following number of shares: Mr. Day -- 36,364 shares; Mr.
     Welliver -- 10,000 shares; and Ms. Robertson -- 3,333 shares. One-half of
     the Restricted Shares, which are not subject to performance-based
     conditions, vested on the first anniversary of the award and one-half of
     the Restricted Shares vested on the second anniversary of the award. Dollar
     values of awards of Restricted Shares shown in the table for 1998 include
     two restricted stock awards. Restricted shares were awarded on January 29,
     1998. The dollar values of such awards are based on the closing price of
     the Common Stock on that date ($28.25), and represent the following number
     of shares: Mr. Day - 10,000 shares; Mr. Welliver - 3,500 shares and Ms.
     Robertson - 2,500 shares. One fifth of the Restricted Shares, which are not
     subject to performance-based conditions, vested on the first anniversary of
     the award and one-fifth of the Restricted Shares will vest on each January
     29, 2000, 2001, 2002 and 2003. Restricted shares were awarded on February
     4, 1999 in lieu of bonuses for 1998 and salary increases for 1999. The
     dollar values of such awards are based on the closing price of the Common
     Stock on that date ($13.56), and represent the following number of shares:
     Mr. Day - 50,000 shares; Mr. Welliver - 15,000 shares and Ms. Robertson -
     20,000 shares. One-fifth of the Restricted Shares, which are not subject to
     performance-based conditions, will vest on each February 4, 2000, 2001,
     2002, 2003 and 2004.

(2)  Options represent the right to purchase shares of Common Stock at a fixed
     price per share.

(3)  Consists of Company (or subsidiary) contributions to defined contribution
     plan (and unfunded, nonqualified excess benefit plan) of $9,600, term life
     insurance premiums of $5,454 and directors' fees of $600.

(4)  Consists of Company (or subsidiary) contributions or other allocations to
     defined contribution plan (and unfunded, nonqualified excess benefit plan)
     and term life insurance premiums, respectively, as follows: Mr. Welliver --
     $9,600 and $1,534; and Ms. Robertson -- $9,300 and $0.


                                       10


<PAGE>   13



                The following table sets forth certain information with respect
to options to purchase Common Stock granted during the year ended December 31,
1998 to each of the named executive officers.

                            OPTION/SAR GRANTS IN 1998


<TABLE>
<CAPTION>
                                               INDIVIDUAL GRANTS
                         ------------------------------------------------------       POTENTIAL REALIZABLE VALUE AT
                          NUMBER OF         PERCENT OF                                        ASSUMED
                          SECURITIES          TOTAL                                    ANNUAL RATES OF STOCK PRICE
                          UNDERLYING         OPTIONS                                     APPRECIATION FOR OPTION
                            OPTIONS          GRANTED     EXERCISE                                TERM (1)          
                            GRANTED            TO         PRICE         EXPIRA-        -----------------------------
                          (NUMBER OF        EMPLOYEES      PER           TION          
NAME                        SHARES)          IN 1998      SHARE          DATE            5% (5)           10% (6)
- - ----                      ----------        --------     --------      --------       ------------     ------------
<S>                       <C>              <C>          <C>           <C>            <C>              <C>
James C. Day                 100,000 (2)        2.64%    $ 28.310      1/28/08        $  1,780,000     $  4,511,000
                              50,000 (3)        1.32%    $ 21.625      7/22/08        $    679,750     $  1,723,250
                             100,000 (4)        2.64%    $ 15.625      10/21/08       $    982,500     $  2,490,500

Byron L. Welliver             55,000 (2)        1.45%    $ 28.310      1/28/08        $    979,000     $  2,481,050
                              20,000 (3)         .53%    $ 21.625      7/22/08        $    271,900     $    689,300
                              45,000 (4)        1.19%    $ 15.625      10/21/08       $    442,125     $  1,120,725

Julie J. Robertson            45,000 (2)        1.19%    $ 28.310      1/28/08        $    801,000     $  2,029,950
                              20,000 (3)         .53%    $ 21.625      7/22/08        $    271,900     $    689,300
                              45,000 (4)        1.19%    $ 15.625      10/21/08       $    442,125     $  1,120,725
</TABLE>


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

(1)  The values shown are based on the indicated assumed annual rates of
     appreciation compounded annually. Actual gains realized, if any, on stock
     option exercises and Common Stock holdings are dependent on the future
     performance of the Common Stock and overall stock market conditions. There
     can be no assurance that the values shown in this table will be achieved.

(2)  Represents a single grant of options on January 29, 1998. One-third of the
     options became exercisable on January 29, 1999, and one-third of the
     options becomes exercisable on each of January 29, 2000 and 2001.

(3)  Represents a single grant of options on July 23, 1998. One-third of the
     options becomes exercisable on each of July 23, 1999, 2000 and 2001.

(4)  Represents a single grant of options on October 22, 1998. One-third of the
     options becomes exercisable on each October 22, 1999, 2000 and 2001.

(5)  Reflects an assumed market price per share of Common Stock of $46.11 for
     the grants made in January, $35.22 for the grants made in July and $25.45
     for the grants made in October.

(6)  Reflects an assumed market price per share of Common Stock of $73.42 for
     the grants made in January, $56.09 for the grants made in July and $40.53
     for the grants made in October.


                                       11


<PAGE>   14



      The following table sets forth certain information with respect to the
exercise of options to purchase Common Stock and SARs during the year ended
December 31, 1998, and the unexercised options held at December 31, 1998 and the
value thereof, by each of the named executive officers.

                     AGGREGATED OPTION/SAR EXERCISES IN 1998
                         AND 12/31/98 OPTION/SAR VALUES

<TABLE>
<CAPTION>
                                                               NUMBER OF                      VALUE OF
                                                              SECURITIES                     UNEXERCISED
                          SHARES                              UNDERLYING                    IN-THE-MONEY
                         ACQUIRED                           OPTIONS/SARS AT                OPTIONS/SARS AT
                        ON EXERCISE                        12/31/98 (SHARES)                  12/31/98
                          (NUMBER       VALUE         ---------------------------    ---------------------------
        NAME            OF SHARES)     REALIZED       EXERCISABLE   UNEXERCISABLE    EXERCISABLE   UNEXERCISABLE
- - ---------------------   ----------     --------       -----------   -------------    -----------   -------------
<S>                     <C>           <C>             <C>          <C>              <C>            <C>
James C. Day.........            0    $         0       428,998         400,002       $ 2,569,778   $ 104,002
Byron L. Welliver....       20,000    $   392,865       207,665         169,335       $ 1,336,398   $  41,602
Julie J. Robertson...            0    $         0        81,799         143,001       $   433,488   $  26,002
</TABLE>


DEFINED BENEFIT PLANS

      The defined benefit plans of the Company that cover its executive officers
provide the benefits shown below. The estimates assume that benefits are
received in the form of 10-year certain and life annuity.


                               PENSION PLAN TABLE

<TABLE>
<CAPTION>
                                                           ESTIMATED ANNUAL BENEFITS UPON RETIREMENT
                                               AT AGE 65 AFTER COMPLETION OF THE FOLLOWING YEARS OF SERVICE (2)
        FIVE-YEAR AVERAGE                   ---------------------------------------------------------------------
     ANNUAL COMPENSATION (1)                  15                  20                   25                    30  
     -----------------------                ------              ------               ------                ------
<S>                                        <C>                 <C>                  <C>                   <C>     
      $  125,000..................         $ 30,000            $ 40,000             $ 50,000              $ 60,000
         200,000..................           48,000              64,000               80,000                96,000
         300,000..................           72,000              96,000              120,000               144,000
         400,000..................           96,000             128,000              160,000               192,000
         600,000..................          144,000             192,000              240,000               288,000
         800,000..................          192,000             256,000              320,000               384,000
       1,000,000..................          240,000             320,000              400,000               480,000
       1,400,000..................          336,000             448,000              560,000               672,000
</TABLE>

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

(1)  Benefit amounts under the Noble Drilling Salaried Employees' Retirement
     Plan (and unfunded, nonqualified excess benefit plan) are based on an
     employee's vested percentage, average monthly compensation and number of
     years of benefit service (maximum 30 years). The average monthly
     compensation is defined in the plan generally to mean the participant's
     average monthly rate of compensation from the Company for the five
     successive calendar years which give the highest average monthly rate of
     compensation for the participant. Plan compensation is defined (with
     certain exceptions) to mean basic compensation, bonuses, commissions and
     overtime pay, exclusive of extraordinary compensation but prior to
     reduction for any compensation deferred under a cash or deferred
     arrangement qualifying under Sections 401(k) or 125 of the Internal Revenue
     Code of 1986, as amended. Accordingly, the amounts reported in the Summary
     Compensation Table included elsewhere herein under the table caption
     "Annual Compensation" approximate plan compensation for 1998.

(2)  Retirement benefits shown above are calculated using 1.6 percent of final
     average pay multiplied by years of service. This slightly overstates the
     benefit since that part of the final average pay that is below the Social
     Security "covered compensation" level should be multiplied by 1.0 percent
     instead of 1.6 percent. "Covered compensation" is the average of the Social
     Security Wage Bases during the 35-year period ending with the year the
     employee reaches Social Security Retirement Age. The amount of benefit
     shown is not subject to deductions for Social Security.

     As of December 31, 1998, the named executive officers had the following
approximate credited years of service for retirement purposes: Mr. Day--21; Mr.
Welliver--17; and Ms. Robertson--10.



                                       12


<PAGE>   15



PERFORMANCE GRAPH

      The following graph sets forth the cumulative total stockholder return for
the Common Stock, the NYSE Stock Market Index (U.S. Companies), and a Competitor
Group Index for the years indicated as prescribed by the SEC's rules.

               COMPARISON OF FIVE YEAR CUMULATIVE TOTAL RETURN(1)
        AMONG NOBLE DRILLING CORPORATION, NYSE STOCK MARKET INDEX (U.S.
                    COMPANIES) AND COMPETITOR GROUP INDEX (2)



                                     [GRAPH]

<TABLE>
<CAPTION>
                                  1993        1994      1995        1996       1997        1998
                                  ----        ----      ----        ----       ----        ----
<S>                              <C>         <C>       <C>         <C>        <C>         <C>  
Company                           100         67.1      102.9       227.1      350.0       147.9
Competitor Group Index (3)        100         81.3      163.0       374.0      500.5       153.6
NYSE Stock Market Index           100        100.0      135.5       164.3      218.3       262.0
(U.S. Companies)
</TABLE>


(1)  Total return assuming reinvestment of dividends. Assumes $100 invested on
     January 1, 1994 in Common Stock, NYSE Stock Market Index (U.S. Companies)
     and a Company constructed competitor group index.

(2)  Fiscal year ending December 31.

(3)  In accordance with the SEC's rules, the Company has elected to select a
     group of peer companies on an industry basis for comparison purposes. The
     competitor group is composed of eight industry participants: Atwood
     Oceanics, Inc., Cliffs Drilling Company, Energy Service Company, Inc.
     (ENSCO), Global Marine Inc., Marine Drilling Companies, Inc., R & B Falcon
     Corporation, Rowan Companies, Inc. and Santa Fe International Corporation.
     Cliffs Drilling Company was merged into R & B Falcon Corporation as of
     December 1, 1998 and will be deleted from the peer group in the future.
     Santa Fe International Corporation was added to the peer group for 1998,
     effective from the date its shares became listed for trading (June 10,
     1997), and will replace Cliffs Drilling Company. Total return calculations
     were weighted according to the respective company's market capitalization.


                                       13


<PAGE>   16



SUPPLEMENTAL PERFORMANCE GRAPH

      The Company has elected to include a supplemental performance graph which
compares the cumulative total stockholder return for the Common Stock, the NYSE
Stock Market Index (U.S. Companies) and a Competitor Group Index for the period
indicated below.

              COMPARISON OF ELEVEN YEAR CUMULATIVE TOTAL RETURN (1)
        AMONG NOBLE DRILLING CORPORATION, NYSE STOCK MARKET INDEX (U.S.
                    COMPANIES) AND COMPETITOR GROUP INDEX (2)


                                     [GRAPH]

<TABLE>
<CAPTION>
                                    1987  1988   1989   1990    1991    1992   1993   1994   1995   1996   1997  1998
                                    ----  ----   ----   ----    ----    ----   ----   ----   ----   ----   ----  ----
<S>                                <C>  <C>    <C>    <C>     <C>    <C>    <C>    <C>    <C>    <C>    <C>    <C>  
Company                              100  121.9  231.3  181.3   78.1   110.9  218.8  146.9  225.0  496.9  765.6  323.4
Competitor Group Index (3)           100   88.2  158.9  139.8   80.5    75.7  127.6  103.8  207.9  477.2  638.6  196.0
NYSE Stock Market Index              100  117.6  152.4  145.6  191.2   207.9  229.7  229.6  311.2  377.5  501.4  601.7
(U.S. Companies)
</TABLE>


(1)  Total return assuming reinvestment of dividends. Assumes $100 invested on
     January 1, 1988 in Common Stock, NYSE Stock Market Index (U.S. Companies)
     and a Company constructed competitor group index.

(2)  Fiscal year ending December 31.

(3)  In accordance with the SEC's rules, the Company has elected to select a
     group of peer companies on an industry basis for comparison purposes. The
     competitor group is composed of eight industry participants: Atwood
     Oceanics, Inc., Cliffs Drilling Company, Energy Service Company, Inc.
     (ENSCO), Global Marine Inc., Marine Drilling Companies, Inc., R & B Falcon
     Corporation, Rowan Companies, Inc. and Santa Fe International Corporation.
     Cliffs Drilling Company was merged into R & B Falcon Corporation as of
     December 1, 1998 and will be deleted from the peer group in the future.
     Santa Fe International Corporation was added to the peer group for 1998,
     effective from the date its shares became listed for trading (June 10,
     1997), and will replace Cliffs Drilling Company. Total return calculations
     were weighted according to the respective company's market capitalization.



                                       14


<PAGE>   17



             SECTION 16(a) BENEFICIAL OWNERSHIP REPORTING COMPLIANCE

      Section 16(a) of the Exchange Act requires directors and officers of the
Company, and persons who own more than 10 percent of the Common Stock, to file
with the SEC initial reports of ownership and reports of changes in ownership of
such stock. Directors, officers and beneficial owners of more than 10 percent of
the Common Stock are required by SEC regulations to furnish the Company with
copies of all Section 16(a) forms they file.

      To the Company's knowledge, based solely on a review of the copies of such
reports furnished to the Company and written representations that no other
reports were required, during the year ended December 31, 1998, all Section
16(a) filing requirements applicable to its directors, officers, and beneficial
owners of more than 10 percent of its Common Stock were complied with, except
that Lawrence Chazen filed one late Form 4 with respect to one transaction and
James Fishel filed three late Form 4's with respect to four transactions.

                    PROPOSAL TO INCREASE THE NUMBER OF SHARES
                         AVAILABLE UNDER THE OPTION PLAN

GENERAL

      The Option Plan was adopted by the Board of Directors of the Company in
1991 and approved by stockholders at the 1991 annual meeting of stockholders.
The Option Plan was amended with stockholder approval in both 1994 and 1997. At
a meeting of the Board of Directors held on February 4, 1999, the Board, subject
to stockholder approval, voted to increase by 5,000,000 the aggregate number of
shares of Common Stock available under the Option Plan effective as of February
4, 1999 (the "Plan Increase").

      The purpose of the Option Plan is to assist the Company in attracting and
retaining as officers and key employees of the Company and its affiliates,
persons of training, experience and ability and to furnish additional incentive
to such persons by encouraging them to become owners of Common Stock. The Board
of Directors believes that the success of the Company is greatly dependent on
its ability to attract and retain individuals of outstanding ability who are
motivated to exert their best efforts on behalf of the Company and its
affiliates. The Board has found that the Company's stock option program has been
highly effective in achieving that goal and has concluded that the stock option
program should be continued. The Board of Directors has also concluded that the
number of shares currently available for the grant of stock options by the
Company under the Option Plan is inadequate to permit the continued use of a
long-term equity component in the Company's compensation program and that the
approval of the Option Plan as amended and restated is warranted. Based upon the
recommendation of Towers Perrin, the Board of Directors has approved the Plan
Amendment increasing the number of shares available under the Option Plan by
5,000,000 shares in the aggregate (which represented 3.8 percent of the
Company's outstanding Common Stock as of March 8, 1999).

THE PLAN INCREASE

      As of January 31, 1999, there were outstanding Options covering 7,445,176
shares of Common Stock, and 233,287 shares of Common Stock outstanding as
Restricted Stock which is subject to forfeiture in whole or in part. Only
1,696,054 shares of Common Stock remained available for future grant or award
under the Option Plan as of that date. If the Plan Increase is approved and
ratified by stockholders, the employees of the Company and its affiliates
eligible to participate therein could receive more benefits under the Option
Plan than are currently available to them.

DESCRIPTION OF THE OPTION PLAN

      The material features of the Option Plan, without giving effect to the
Plan Increase, are described below.

      General. Under the Option Plan, shares of Common Stock may be subject to
grants of Incentive Options, Nonqualified Options, Stock Appreciation Rights
("SARs") or awards of Restricted Stock to officers and other employees of the
Company and its affiliates. Options and any SARs related thereto may be granted,
and Restricted Stock may be awarded, until the 10,700,000 shares of Common Stock
available under the Option Plan have been exhausted or the Option Plan has been
terminated. Shares of Common Stock covered by an Option that expires or
terminates prior to exercise and shares of Restricted Stock returned to the
Company are again available for grant of

                                       15


<PAGE>   18



Options and awards of Restricted Stock. The Option Plan contains antidilution
provisions applicable in the event of increase or decrease in the number of
outstanding shares of Common Stock, effected without receipt of consideration
therefor by the Company, through a stock dividend or any recapitalization or
merger or otherwise in which the Company is the surviving corporation, resulting
in a stock split-up, combination or exchange of shares of the Company, in which
event appropriate adjustments will be made in the maximum number of shares
subject to the Option Plan and the number of shares and option prices under then
outstanding Options.

      Administration. The Option Plan is administered by a committee (the
"Committee") of the Board of Directors of the Company. The Committee must
consist of two or more directors of the Company, all of whom must be Non-
Employee Directors as defined in Rule 16b-3 under the Exchange Act and Outside
Directors within the meaning of Section 162(m) of the Internal Revenue Code of
1986, as amended (the "Code"), and the regulations promulgated thereunder. The
Committee determines the grants of Options and awards of Restricted Stock, the
terms and provisions of the respective agreements covering such grants or awards
and all other decisions concerning the Option Plan. It is impracticable to
estimate the total number of officers and employees eligible to participate in
the Option Plan. The Option Plan provides that the determination of the
Committee is binding with respect to all questions of interpretation and
application of the Option Plan and of Options granted or awards of Restricted
Stock made thereunder, subject to the express provisions of the Option Plan and
except as set forth below under "Stock Options and SARs" and "Amendment of the
Option Plan."

      Stock Options and SARs. The Option Plan provides that, from time to time
during the term of the Option Plan, the Committee, in its sole discretion, may
grant Incentive Options, Nonqualified Options, Restricted Stock or any
combination thereof to any employee eligible under the Option Plan. Each person
who accepts an Option shall enter into an agreement with the Company whereupon
such person shall become a participant in the Option Plan in accordance with the
terms of such agreement.

      The Committee may from time to time grant SARs in conjunction with all or
any portion of an Option either at the time of the initial Option grant or, with
respect to a Nonqualified Option, at any time after the initial Option grant
while the Nonqualified Option is outstanding. SARs generally will be subject to
the same terms and conditions and exercisable to the same extent as Options, as
described above. SARs entitle an Optionee to receive without payment to the
Company (except for applicable withholding taxes) the excess of the aggregate
fair market value per share with respect to which the SAR is then being
exercised (determined as of the date of such exercise) over the aggregate
purchase price of such shares as provided in the related Option. Payment may be
made in shares of Common Stock or in cash, or a combination thereof, as
determined by the Committee.

      Option Price. The option price for each Share covered by an Incentive
Option shall not be less than the greater of (a) the par value of such Share or
(b) the Fair Market Value (as defined in the Option Plan) of such Share at the
time such Option is granted. The option price for each Share covered by a
Nonqualified Option shall not be less than the greater of (a) the par value of
such Share or (b) 100 percent of the Fair Market Value of such Share at the time
the Option is granted, except that the minimum option price may be equal to or
greater than 85 percent of the Fair Market Value of such Share at the time the
Option is granted if and to the extent the discount from Fair Market Value is
expressly granted in lieu of a reasonable amount of salary or cash bonus. If the
Company agrees to substitute a new Option under the Option Plan for an old
Option, or to assume an old Option, as provided for in the Option Plan, the
option price of the Shares covered by each such new Option or assumed Option may
be otherwise determined by a formula; provided, however, in no event shall: (a)
the excess of the aggregate Fair Market Value of the Shares subject to the
Option immediately after the substitution or assumption over the aggregate
option price of such Shares be more than the excess of the aggregate Fair Market
Value of all Shares subject to the Option immediately prior to the substitution
or assumption over the aggregate option price of such Shares; (b) in the case of
an Incentive Option, the new Option or the assumption of the old Option give the
Optionee additional benefits that he would not have under the old Option; or (c)
the ratio of the option price to the Fair Market Value of the stock subject to
the Option immediately after the substitution or assumption be more favorable to
the Optionee than the ratio of the option price to the Fair Market Value of the
stock subject to the old Option immediately prior to such substitution or
assumption, on a Share by Share basis. Notwithstanding the foregoing, the new
option price in the case of an Incentive Option shall be subject to the
requirements of Section 424(a) of the Code and the Treasury regulations and
revenue rulings promulgated thereunder.


                                       16


<PAGE>   19



      Restricted Stock. The Option Plan provides that Restricted Stock may be
awarded by the Committee to such eligible recipients as it may determine from
time to time. The eligible recipients are those individuals who are eligible for
Option grants. Restricted Stock is Common Stock that may not be sold, assigned,
transferred, discounted, exchanged, pledged or otherwise encumbered or disposed
of until the restrictions, terms and conditions, including forfeitures, if any,
set by the Committee, which may include, among other things, the achievement of
specific goals, have been satisfied (the "Restricted Period"). During the
Restricted Period, unless specifically provided otherwise in accordance with the
terms of the Option Plan, the recipient of Restricted Stock would be the record
owner of such shares and have all the rights of a stockholder with respect to
such shares, including the right to vote and the right to receive dividends or
other distributions made or paid with respect to such shares.

      The Option Plan provides that the Committee has the authority to cancel
all or any portion of any outstanding restrictions prior to the expiration of
the Restricted Period with respect to any and all of the shares of Restricted
Stock awarded to an individual on such terms and conditions as the Committee may
deem appropriate. If during the Restricted Period an individual's continuous
employment terminates for any reason, any Restricted Stock remaining subject to
restrictions will be forfeited by the individual and transferred at no cost to
the Company; provided, however, that as noted above, the Committee has the
authority to cancel any or all outstanding restrictions prior to the end of the
Restricted Period, including the cancellation of restrictions in connection with
certain types of termination of employment.

      Amendment of the Option Plan. The Board of Directors may at any time
amend, suspend or terminate the Option Plan; provided, however, the Board may
not, without approval of the stockholders of the Company, amend the Option Plan
so as to (i) increase the maximum number of shares subject thereto, or (ii)
reduce the option price per share covered by Options granted under the Option
Plan below the price specified in the Option Plan. Additionally, the Board may
not modify, impair or cancel any outstanding Option or SARs related thereto, or
the restrictions, terms or conditions applicable to Shares of Restricted Stock,
without the consent of the holder thereof.

UNITED STATES FEDERAL INCOME TAX CONSEQUENCES

      The following summary is based upon an analysis of the Code, existing
laws, judicial decisions, administrative rulings, regulations and proposed
regulations, all of which are subject to change. Moreover, the following is only
a summary of United States federal income tax consequences and such consequences
may be either more or less favorable than those described below depending on a
an employee's particular circumstances.

      Incentive Options. No income will be recognized by an Optionee for federal
income tax purposes upon the grant or exercise of an Incentive Option; provided,
however, that to the extent that an Incentive Option is exercised more than
three months (twelve months in the event of disability) from the date of
termination of employment for any reason other than death, such Incentive Option
will be taxed in the same manner described below for Nonqualified Options
(rather than in the manner described herein for an Incentive Option). The basis
of shares transferred to an Optionee pursuant to the exercise of an Incentive
Option is the price paid for the shares. If the Optionee holds the shares for at
least one year after transfer of the shares to the Optionee and two years after
the grant of the Incentive Option, the Optionee will recognize capital gain or
loss upon sale of the shares received upon the exercise equal to the difference
between the amount realized on the sale and the basis of the stock. Generally,
if the shares are not held for that period, the Optionee will recognize ordinary
income upon disposition in an amount equal to the excess of the fair market
value of the shares on the date of exercise over the amount paid for such
shares, or if less (and if the disposition is a transaction in which loss, if
sustained, would be recognized), the gain on disposition. Any additional gain or
loss realized by the Optionee upon such disposition will be a capital gain or
loss.

      The excess of the fair market value of shares received upon the exercise
of an Incentive Option over the option price for the shares is an item of
adjustment for the Optionee for purposes of the alternative minimum tax.

      The Company is not entitled to a deduction upon the exercise of an
Incentive Option by an Optionee. If the Optionee disposes of the shares received
pursuant to such exercise prior to the expiration of one year following transfer
of the shares to the Optionee or two years after grant of the option, however,
the Company may, subject to the deduction limitations described below, deduct an
amount equal to the ordinary income recognized by the Optionee upon disposition
of the shares at the time such income is recognized by the Optionee.

                                       17


<PAGE>   20



      If an Optionee uses already owned shares of Common Stock to pay the
exercise price for shares under an Incentive Option, the resulting tax
consequences will depend upon whether the already owned shares of Common Stock
are "statutory option stock", and, if so, whether such statutory option stock
has been held by the Optionee for the applicable holding period referred to in
Section 424(c)(3)(A) of the Code. In general, "statutory option stock" (as
defined in Section 424(c)(3)(B) of the Code) is any stock acquired through the
exercise of an Incentive Option, a qualified stock option, an option granted
pursuant to an employee stock purchase plan or restricted stock option, but not
stock acquired through the exercise of a nonstatutory option. If the stock is
statutory option stock with respect to which the applicable holding period has
been satisfied, no income will be recognized by the Optionee upon the transfer
of such stock in payment of the exercise price of an Incentive Option. If the
stock is not statutory option stock, no income will be recognized by the
Optionee upon the transfer of the stock unless the stock is not substantially
vested within the meaning of the regulations under Section 83 of the Code (in
which event it appears that the Optionee will recognize ordinary income upon the
transfer equal to the amount by which the fair market value of the transferred
shares exceeds their basis). If the stock used to pay the exercise price of an
Incentive Option is statutory option stock with respect to which the applicable
holding period has not been satisfied, the transfer of such stock will be a
disqualifying disposition described in Section 421(b) of the Code which will
result in the recognition of ordinary income by the Optionee in an amount equal
to the excess of the fair market value of the statutory option stock at the time
the Incentive Option covering such stock was exercised over the amount paid for
such stock. Under the present provisions of the Code, it is not clear whether
all shares received upon the exercise of an Incentive Option with already-owned
shares will be statutory option stock or how the Optionee's basis will be
allocated among such shares.

      Nonqualified Options. No income will be recognized by an Optionee for
federal income tax purposes upon the grant of a Nonqualified Option. Upon
exercise of a Nonqualified Option, the Optionee will recognize ordinary income
in an amount equal to the excess of the fair market value of the shares on the
date of exercise over the amount paid for such shares. Income recognized upon
the exercise of Nonqualified Options will be considered compensation subject to
withholding at the time the income is recognized, and, therefore, the Company
must make the necessary arrangements with the Optionee to ensure that the amount
of the tax required to be withheld is available for payment. Nonqualified
Options are designed to provide the Company with a deduction equal to the amount
of ordinary income recognized by the Optionee at the time of such recognition by
the Optionee, subject to the deduction limitations described below.

      The basis of shares transferred to an Optionee pursuant to exercise of a
Nonqualified Option is the price paid for such shares plus an amount equal to
any income recognized by the Optionee as a result of the exercise of the option.
If an Optionee thereafter sells shares acquired upon exercise of a Nonqualified
Option, any amount realized over the basis of the shares will constitute capital
gain to the Optionee for federal income tax purposes.

      If an Optionee uses already owned shares of Common Stock to pay the
exercise price for shares under a Nonqualified Option, the number of shares
received pursuant to the Nonqualified Option which is equal to the number of
shares delivered in payment of the exercise price will be considered received in
a nontaxable exchange, and the fair market value of the remaining shares
received by the Optionee upon the exercise will be taxable to the Optionee as
ordinary income. If the already owned shares of Common Stock are not "statutory
option stock" or are statutory option stock with respect to which the applicable
holding period referred to in Section 424(c)(3)(A) of the Code has been
satisfied, the shares received pursuant to the exercise of the Nonqualified
Option will not be statutory option stock and the Optionee's basis in the number
of shares received in exchange for the stock delivered in payment of the
exercise price will be equal to the basis of the shares delivered in payment.
The basis of the remaining shares received upon the exercise will be equal to
the fair market value of the shares. However, if the already owned shares of
Common Stock are statutory option stock with respect to which the applicable
holding period has not been satisfied, it is not presently clear whether the
exercise will be considered a disqualifying disposition of the statutory option
stock, whether the shares received upon such exercise will be statutory option
stock, or how the Optionee's basis will be allocated among the shares received.

      SARs. There will be no federal income tax consequences to either the
recipient or the Company upon the grant of SARs. Generally, the recipient will
recognize ordinary income subject to withholding upon the exercise of SARs in an
amount equal to the amount of cash received and the fair market value of any
shares acquired pursuant to the exercise. Subject to the deduction limitations
described below, the Company generally will be entitled to a corresponding tax
deduction equal to the amount includable in the recipient's income.


                                       18


<PAGE>   21



      Restricted Stock. If the restrictions on an award of Restricted Stock are
of a nature that such shares are both subject to a substantial risk of
forfeiture and are not freely transferable within the meaning of Section 83 of
the Code, the recipient will not recognize income for federal income tax
purposes at the time of the award unless such recipient affirmatively elects to
include the fair market value of the shares of restricted stock on the date of
the award, less any amount paid therefor, in gross income for the year of the
award pursuant to Section 83(b) of the Code. In the absence of such an election,
the recipient will be required to include in income for federal income tax
purposes in the year in which occurs the date the shares either become freely
transferable or are no longer subject to a substantial risk of forfeiture within
the meaning of Section 83 of the Code, the fair market value of the shares of
restricted stock on such date, less any amount paid therefor. The Company will
be entitled to a deduction at the time of income recognition to the recipient in
an amount equal to the amount the recipient is required to include in income
with respect to the shares, subject to the deduction limitations described
below. If a Section 83(b) election is made within 30 days after the date the
Restricted Stock is received, the recipient will recognize ordinary income at
the time of the receipt of the Restricted Stock and the Company will be entitled
to a corresponding deduction equal to the fair market value (determined without
regard to applicable restrictions) of the shares at such time less the amount
paid, if any, by the recipient for the Restricted Stock. If a Section 83(b)
election is made, no additional income will be recognized by the recipient upon
the lapse of restrictions on the Restricted Stock, but, if the Restricted Stock
is subsequently forfeited, no deduction will be allowed to the recipient with
respect to such forfeiture. Dividends paid to a recipient holding restricted
stock before the expiration of the restriction period will be additional
compensation taxable as ordinary income to the recipient, unless the recipient
made an election under Section 83(b). Subject to the deduction limitations
described below, the Company generally will be entitled to a corresponding tax
deduction equal to the dividends includable in the recipient's income as
compensation. If the recipient has made a Section 83(b) election, the dividends
will be dividend income, rather than additional compensation, to the recipient.

      If the restrictions on an award of Restricted Stock are not of a nature
that such shares are both subject to a substantial risk of forfeiture and not
freely transferable, within the meaning of Section 83 of the Code, the recipient
will recognize ordinary income for federal income tax purposes at the time of
the award in an amount equal to the fair market value of the shares of
Restricted Stock on the date of the award, less any amount paid therefor. The
Company will be entitled to a deduction at such time in an amount equal to the
amount the recipient is required to include in income with respect to the
shares, subject to the deduction limitations described below.

      Limitations on the Company's Compensation Deduction. Section 162(m) of the
Code limits the deduction that the Company may take for otherwise deductible
compensation payable to certain officers of the Company to the extent that
compensation paid to any such officer for such year exceeds $1 million, unless
such compensation is performance-based, is approved by the Company's
stockholders, and meets certain other criteria. Compensation attributable to a
stock option or SAR is deemed to satisfy the requirements for performance-based
compensation if (i) the grant or award is made by a compensation committee
composed of two or more outside directors; (ii) the plan under which the option
or right is granted states the maximum number of shares with respect to which
options or rights may be granted during a specified period to any employee; and
(iii) under the terms of the option or right, the amount of compensation the
employee could receive is based solely on an increase in the value of the stock
after the date of the grant or award. The Option Plan as amended and restated
has been designed to enable awards of Options (other than Nonqualified Options
granted at less than fair market value on the date of grant) and SARs granted by
the Committee to qualify as performance-based compensation for purposes of
Section 162(m) of the Code.

                                    AUDITORS

      The Board of Directors has appointed PricewaterhouseCoopers LLP, which has
audited the Company's financial statements since October 7, 1994, to audit the
financial statements of the Company for the year ending December 31, 1999. Such
appointment will not be submitted to stockholders for ratification or approval.
Representatives of PricewaterhouseCoopers LLP are expected to be present at the
meeting to respond to appropriate questions from the stockholders and will be
given the opportunity to make a statement should they desire to do so.



                                       19


<PAGE>   22


                     STOCKHOLDER PROPOSALS AND OTHER MATTERS

      Stockholder proposals for inclusion in the Company's proxy materials in
connection with the 2000 annual meeting of stockholders, which is currently
scheduled to be held on April 27, 2000, must be received by the Company at its
office in Houston, Texas, addressed to the Secretary of the Company, no later
than November 19, 1999.

      The cost of solicitation of proxies will be borne by the Company. The
Company has employed Corporate Investor Communications, Inc. to solicit proxies
from brokers, bank nominees, institutional holders and individual holders for
use at the meeting at a fee not to exceed $5,500 plus certain expenses. In
addition, certain officers and employees of the Company, who will receive no
additional compensation for their services, may solicit proxies in person or by
mail, telephone, facsimile telecommunication or telegraph.

      The Board of Directors does not intend to present any other matter at the
meeting and knows of no other matters that will be presented. However, if any
other matter comes before the meeting, the persons named in the enclosed proxy
intend to vote thereon in accordance with their best judgment.

                                                 NOBLE DRILLING CORPORATION

                                                        James C. Day
                                                        Chairman and
                                                   Chief Executive Officer
Houston, Texas
March 22, 1999



                                       20




<PAGE>   23
                           NOBLE DRILLING CORPORATION
                                        
          THIS PROXY IS SOLICITED ON BEHALF OF THE BOARD OF DIRECTORS



     The undersigned hereby appoints James C. Day and Robert D. Campbell, and
each of them, proxies with power of substitution in each, and hereby authorizes
them to represent and to vote, as designated below, all shares of Common Stock
of Noble Drilling Corporation (the "Company") standing in the name of the
undersigned on March 8, 1999, at the annual meeting of stockholders to be held
on April 22, 1999 at 10:00a.m. in Houston, Texas, and at any adjournment thereof
and especially to vote on the items of business specified below, as more fully
described in the notice of the meeting and the proxy statement accompanying the
same, receipt of which is hereby acknowledged.

<TABLE>
<S>                       <C>                             <C>
1. ELECTION OF DIRECTORS  FOR all nominees listed below   WITHHOLD AUTHORITY
                          (except as marked to the        to vote for all nominees
                          contrary below) [ ]             listed below [ ]

   LAWRENCE J. CHAZEN     WILLIAM J. DORE                 WILLIAM A. SEARS

    (INSTRUCTION: To withhold authority to vote for any individual nominee,
    write the nominee's name in the space provided below.)


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


2. Proposal to increase by 5,000,000 the number of shares of Common Stock
   available under the Company's 1991 Stock Option and Restricted Stock Plan:


                 FOR [ ]        AGAINST [ ]         ABSTAIN [ ]

3. In their discretion, the proxies are authorized to vote upon such other 
business or matters as may properly come before the meeting or any adjournment 
thereof.
</TABLE>

                (CONTINUED AND TO BE SIGNED ON THE REVERSE SIDE)

<PAGE>   24
     THIS PROXY, WHEN DULY EXECUTED AND RETURNED, WILL BE VOTED IN THE MANNER 
DESIGNATED HEREIN BY THE UNDERSIGNED STOCKHOLDER. IF THIS PROXY IS DULY 
EXECUTED AND RETURNED, BUT WITHOUT A CLEAR VOTING DESIGNATION, IT WILL BE VOTED 
FOR ITEMS 1 AND 2.

     The undersigned hereby revokes any proxy or proxies heretofore given to 
represent or vote such Common Stock and hereby ratifies and confirms all 
actions that said proxies, their substitutes, or any of them, may lawfully take 
in accordance with the terms hereof.




                                   Dated:________________________________, 1999

                                   ____________________________________________

                                   ____________________________________________
                                   Signature(s) of Stockholder(s)

                                   This proxy should be signed exactly as your
                                   name appears hereon. Joint owners should both
                                   sign. If signed as attorney, executor,
                                   guardian or in some other representative
                                   capacity, or as officer of a corporation,
                                   please indicate your capacity or title.

                                   Please complete, date and sign this proxy and
                                   return it promptly in the enclosed envelope,
                                   which requires no postage if mailed in the
                                   United States.






                                       2
<PAGE>   25
                           NOBLE DRILLING CORPORATION
                                        
                    VOTING INSTRUCTION CARD FOR COMMON STOCK
                                        
       VOTING INSTRUCTIONS SOLICITED ON BEHALF OF THE BOARD OF DIRECTORS



     The undersigned hereby instructs the trustee to vote, as designated below,
all shares of Common Stock of Noble Drilling Corporation that are credited to
the accounts of the undersigned (whether or not vested) in the Noble Drilling
Corporation 401(k) Savings Plan at the annual meeting of stockholders to be
held on April 22, 1999 at 10:00 a.m. in Houston, Texas, and at any adjournment
thereof and especially to vote on the items of business specified below, as more
fully described in the notice of the meeting and the proxy statement
accompanying the same, receipt of which is hereby acknowledged.

<TABLE>
<S>                       <C>                             <C>
1. ELECTION OF DIRECTORS  FOR all nominees listed below   WITHHOLD AUTHORITY
                          (except as marked to the        to vote for all nominees
                          contrary below) [ ]             listed below [ ]

   LAWRENCE J. CHAZEN     WILLIAM J. DORE                 WILLIAM A. SEARS

    (INSTRUCTION: To withhold authority to vote for any individual nominee,
    write the nominee's name in the space provided below.)


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


2. Proposal to increase by 5,000,000 the number of shares of Common Stock
   available under the Company's 1991 Stock Option and Restricted Stock Plan:


                 FOR [ ]        AGAINST [ ]         ABSTAIN [ ]

3. In their discretion, the proxies are authorized to vote upon such other 
   business or matters as may properly come before the meeting or any 
   adjournment thereof.
</TABLE>

                (CONTINUED AND TO BE SIGNED ON THE REVERSE SIDE)







                                       1
<PAGE>   26
     THIS VOTING INSTRUCTION CARD, WHEN DULY EXECUTED AND RETURNED, WILL BE
VOTED BY THE TRUSTEE OF THE NOBLE DRILLING CORPORATION 401(k) SAVINGS PLAN
("401(k) PLAN") IN THE MANNER DESIGNATED HEREIN BY THE UNDERSIGNED 401(k)
PARTICIPANT. IF THIS VOTING INSTRUCTION CARD IS DULY EXECUTED AND RETURNED, BUT
WITHOUT A CLEAR VOTING DESIGNATION, IT WILL BE VOTED FOR ITEMS 1 AND 2.






                                   Dated:________________________________, 1999

                                   ____________________________________________

                                   ____________________________________________
                                   Signature(s) of Stockholder(s)401(k) Plan
                                    Participant

                                   This voting instruction card should be signed
                                   exactly as your name appears hereon.

                                   Please complete, date and sign this voting
                                   instruction card and return it promptly in
                                   the enclosed envelope, which requires no
                                   postage if mailed in the United States.





                                       2


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