<PAGE>   1
                                                                  Exhibit 24.1


                       MARINE DRILLING COMPANIES, INC.

                              POWER OF ATTORNEY



WHEREAS, Marine Drilling Companies, Inc., a Texas corporation (the "Company"),
intends to file with the Securities and Exchange Commission (the "Commission")
under the Securities Exchange Act of 1934, as amended, an annual report on Form
10-K for the year ended December 31, 1996 and quarterly reports on Form 10-Q for
the quarters ended March 31, June 30 and September 30, 1997, with such amendment
or amendments thereto in each case as may be necessary or appropriate, together
with any and all exhibits and other documents having relation to said reports;

NOW, THEREFORE, the undersigned in his capacity as a director of the Company,
does hereby appoint each of William H. Flores and Joan R. Smith, signing singly,
the undersigned's true and lawful attorney with power to act with full power of
substitution and resubstitution, to execute in his name, place and stead, in his
capacity as Director the reports referred to above, together with any and all
amendments thereto as said attorney shall deem necessary or incidental in
connection therewith, and to file the same with the Commission. Such attorney
shall have full power and authority to do and perform in the name and on behalf
of the undersigned, in any and all capacities every act whatsoever necessary or
desirable to be done in the premises, as fully and to all intents and purposes
as the undersigned might or could do in person, the undersigned hereby ratifying
and approving the acts of such attorney.

IN WITNESS WHEREOF, the undersigned has executed this instrument as of this 13th
day of February 1997.

                                                     /s/ ROBERT L. BARBANELL
                                                     -------------------------
                                                     Robert L. Barbanell





<PAGE>   2





                                                                   Exhibit 24.1


                       MARINE DRILLING COMPANIES, INC.

                              POWER OF ATTORNEY



WHEREAS, Marine Drilling Companies, Inc., a Texas corporation (the "Company"),
intends to file with the Securities and Exchange Commission (the "Commission")
under the Securities Exchange Act of 1934, as amended, an annual report on Form
10-K for the year ended December 31, 1996 and quarterly reports on Form 10-Q for
the quarters ended March 31, June 30 and September 30, 1997, with such amendment
or amendments thereto in each case as may be necessary or appropriate, together
with any and all exhibits and other documents having relation to said reports;

NOW, THEREFORE, the undersigned in his capacity as a director of the Company,
does hereby appoint each of William H. Flores and Joan R. Smith, signing singly,
the undersigned's true and lawful attorney with power to act with full power of
substitution and resubstitution, to execute in his name, place and stead, in his
capacity as Director the reports referred to above, together with any and all
amendments thereto as said attorney shall deem necessary or incidental in
connection therewith, and to file the same with the Commission. Such attorney
shall have full power and authority to do and perform in the name and on behalf
of the undersigned, in any and all capacities every act whatsoever necessary or
desirable to be done in the premises, as fully and to all intents and purposes
as the undersigned might or could do in person, the undersigned hereby ratifying
and approving the acts of such attorney.

IN WITNESS WHEREOF, the undersigned has executed this instrument as of this 13th
day of February 1997.

                                                    /s/ DAVID A.B. BROWN
                                                    ----------------------
                                                    David A.B. Brown




<PAGE>   3






                                                                   Exhibit 24.1


                       MARINE DRILLING COMPANIES, INC.

                              POWER OF ATTORNEY



WHEREAS, Marine Drilling Companies, Inc., a Texas corporation (the "Company"),
intends to file with the Securities and Exchange Commission (the "Commission")
under the Securities Exchange Act of 1934, as amended, an annual report on Form
10-K for the year ended December 31, 1996 and quarterly reports on Form 10-Q for
the quarters ended March 31, June 30 and September 30, 1997, with such amendment
or amendments thereto in each case as may be necessary or appropriate, together
with any and all exhibits and other documents having relation to said reports;

NOW, THEREFORE, the undersigned in his capacity as a director of the Company,
does hereby appoint each of William H. Flores and Joan R. Smith, signing singly,
the undersigned's true and lawful attorney with power to act with full power of
substitution and resubstitution, to execute in his name, place and stead, in his
capacity as Director the reports referred to above, together with any and all
amendments thereto as said attorney shall deem necessary or incidental in
connection therewith, and to file the same with the Commission. Such attorney
shall have full power and authority to do and perform in the name and on behalf
of the undersigned, in any and all capacities every act whatsoever necessary or
desirable to be done in the premises, as fully and to all intents and purposes
as the undersigned might or could do in person, the undersigned hereby ratifying
and approving the acts of such attorney.

IN WITNESS WHEREOF, the undersigned has executed this instrument as of this 13th
day of February 1997.

                                                        /s/ HOWARD I. BULL
                                                        --------------------
                                                        Howard I. Bull






<PAGE>   4




                                                                   Exhibit 24.1


                       MARINE DRILLING COMPANIES, INC.

                              POWER OF ATTORNEY



WHEREAS, Marine Drilling Companies, Inc., a Texas corporation (the "Company"),
intends to file with the Securities and Exchange Commission (the "Commission")
under the Securities Exchange Act of 1934, as amended, an annual report on Form
10-K for the year ended December 31, 1996 and quarterly reports on Form 10-Q for
the quarters ended March 31, June 30 and September 30, 1997, with such amendment
or amendments thereto in each case as may be necessary or appropriate, together
with any and all exhibits and other documents having relation to said reports;

NOW, THEREFORE, the undersigned in his capacity as a director of the Company,
does hereby appoint each of William H. Flores and Joan R. Smith, signing singly,
the undersigned's true and lawful attorney with power to act with full power of
substitution and resubstitution, to execute in his name, place and stead, in his
capacity as Director the reports referred to above, together with any and all
amendments thereto as said attorney shall deem necessary or incidental in
connection therewith, and to file the same with the Commission. Such attorney
shall have full power and authority to do and perform in the name and on behalf
of the undersigned, in any and all capacities every act whatsoever necessary or
desirable to be done in the premises, as fully and to all intents and purposes
as the undersigned might or could do in person, the undersigned hereby ratifying
and approving the acts of such attorney.

IN WITNESS WHEREOF, the undersigned has executed this instrument as of this 13th
day of February 1997.

                                                    /s/ NATHANIEL A. GREGORY
                                                    ------------------------
                                                    Nathaniel A. Gregory





<PAGE>   5





                                                                   Exhibit 24.1


                       MARINE DRILLING COMPANIES, INC.

                              POWER OF ATTORNEY



WHEREAS, Marine Drilling Companies, Inc., a Texas corporation (the "Company"),
intends to file with the Securities and Exchange Commission (the "Commission")
under the Securities Exchange Act of 1934, as amended, an annual report on Form
10-K for the year ended December 31, 1996 and quarterly reports on Form 10-Q for
the quarters ended March 31, June 30 and September 30, 1997, with such amendment
or amendments thereto in each case as may be necessary or appropriate, together
with any and all exhibits and other documents having relation to said reports;

NOW, THEREFORE, the undersigned in his capacity as a director of the Company,
does hereby appoint each of William H. Flores and Joan R. Smith, signing singly,
the undersigned's true and lawful attorney with power to act with full power of
substitution and resubstitution, to execute in his name, place and stead, in his
capacity as Director the reports referred to above, together with any and all
amendments thereto as said attorney shall deem necessary or incidental in
connection therewith, and to file the same with the Commission. Such attorney
shall have full power and authority to do and perform in the name and on behalf
of the undersigned, in any and all capacities every act whatsoever necessary or
desirable to be done in the premises, as fully and to all intents and purposes
as the undersigned might or could do in person, the undersigned hereby ratifying
and approving the acts of such attorney.

IN WITNESS WHEREOF, the undersigned has executed this instrument as of this 13th
day of February 1997.

                                                  /s/ CHRISTOPHER M. LINNEMAN
                                                  ----------------------------
                                                  Christopher M. Linneman