<PAGE>   1
                                                                      EXHIBIT 24

                                POWER OF ATTORNEY


                  I JERRY M. ARMSTRONG, in my individual capacity and as a
director of Pogo Producing Company (the "Company"), do hereby appoint PAUL G.
VAN WAGENEN and THOMAS E. HART, and each of them severally, my true and lawful
attorney or attorneys with power to act with or without the other, and with full
power of substitution and resubstitution, to prepare, execute and file, in my
name, place and stead in my individual capacity and as a director of the
Company, such documents, reports and filings as may be necessary or advisable
under the Securities Exchange Act of 1934, as amended (the "Act"), the
Securities Act of 1933, as amended (the "Securities Act") or any other federal,
state or local law regulating the Company including, without limitation, the
Company's Annual Report of Form 10-K for the fiscal year ended December 31,
1999, as prescribed by the Securities and Exchange Commission (the "Commission")
pursuant to the Act, and the rules and regulations promulgated thereunder, with
any and all exhibits and other documents relating thereto, any and all
amendments to said Annual Report and all instruments as said attorneys or any of
them shall deem necessary or incidental in connection therewith and to file the
same with the Commission.

                  Each of said attorneys shall have full power and authority to
do and perform in my name and on my behalf any act whatsoever to accomplish the
purpose and intent of the forgoing that said attorneys deem may be necessary or
desirable to be done in the premises as fully and to all intents and purposes as
I might or could do in person, and by my signature hereto, I hereby ratify and
approve any and all of such acts of said attorneys and each of them.

                  IN WITNESS WHEREOF, I have executed this instrument on this
25th day of January, 2000.



                                             /s/ JERRY M. ARMSTRONG
                                             ----------------------------------
                                             Jerry M. Armstrong


<PAGE>   2



                                POWER OF ATTORNEY



                  I TOBIN ARMSTRONG, in my individual capacity and as a director
of Pogo Producing Company (the "Company"), do hereby appoint PAUL G. VAN WAGENEN
and THOMAS E. HART, and each of them severally, my true and lawful attorney or
attorneys with power to act with or without the other, and with full power of
substitution and resubstitution, to prepare, execute and file, in my name, place
and stead in my individual capacity and as a director of the Company, such
documents, reports and filings as may be necessary or advisable under the
Securities Exchange Act of 1934, as amended (the "Act"), the Securities Act of
1933, as amended (the "Securities Act") or any other federal, state or local law
regulating the Company including, without limitation, the Company's Annual
Report of Form 10-K for the fiscal year ended December 31, 1999, as prescribed
by the Securities and Exchange Commission (the "Commission") pursuant to the
Act, and the rules and regulations promulgated thereunder, with any and all
exhibits and other documents relating thereto, any and all amendments to said
Annual Report and all instruments as said attorneys or any of them shall deem
necessary or incidental in connection therewith and to file the same with the
Commission.

                  Each of said attorneys shall have full power and authority to
do and perform in my name and on my behalf any act whatsoever to accomplish the
purpose and intent of the forgoing that said attorneys deem may be necessary or
desirable to be done in the premises as fully and to all intents and purposes as
I might or could do in person, and by my signature hereto, I hereby ratify and
approve any and all of such acts of said attorneys and each of them.

                  IN WITNESS WHEREOF, I have executed this instrument on this
25th day of January, 2000.



                                               /s/ TOBIN ARMSTRONG
                                               --------------------------------
                                               Tobin Armstrong


<PAGE>   3



                                POWER OF ATTORNEY



                  I JACK S. BLANTON, in my individual capacity and as a director
of Pogo Producing Company (the "Company"), do hereby appoint PAUL G. VAN WAGENEN
and THOMAS E. HART, and each of them severally, my true and lawful attorney or
attorneys with power to act with or without the other, and with full power of
substitution and resubstitution, to prepare, execute and file, in my name, place
and stead in my individual capacity and as a director of the Company, such
documents, reports and filings as may be necessary or advisable under the
Securities Exchange Act of 1934, as amended (the "Act"), the Securities Act of
1933, as amended (the "Securities Act") or any other federal, state or local law
regulating the Company including, without limitation, the Company's Annual
Report of Form 10-K for the fiscal year ended December 31, 1999, as prescribed
by the Securities and Exchange Commission (the "Commission") pursuant to the
Act, and the rules and regulations promulgated thereunder, with any and all
exhibits and other documents relating thereto, any and all amendments to said
Annual Report and all instruments as said attorneys or any of them shall deem
necessary or incidental in connection therewith and to file the same with the
Commission.

                  Each of said attorneys shall have full power and authority to
do and perform in my name and on my behalf any act whatsoever to accomplish the
purpose and intent of the forgoing that said attorneys deem may be necessary or
desirable to be done in the premises as fully and to all intents and purposes as
I might or could do in person, and by my signature hereto, I hereby ratify and
approve any and all of such acts of said attorneys and each of them.

                  IN WITNESS WHEREOF, I have executed this instrument on this 25
day of January, 2000.



                                               /s/ JACK S. BLANTON
                                               --------------------------------
                                               Jack S. Blanton


<PAGE>   4



                                POWER OF ATTORNEY



                  I W. M. BRUMLEY, JR., in my individual capacity and as a
director of Pogo Producing Company (the "Company"), do hereby appoint PAUL G.
VAN WAGENEN and THOMAS E. HART, and each of them severally, my true and lawful
attorney or attorneys with power to act with or without the other, and with full
power of substitution and resubstitution, to prepare, execute and file, in my
name, place and stead in my individual capacity and as a director of the
Company, such documents, reports and filings as may be necessary or advisable
under the Securities Exchange Act of 1934, as amended (the "Act"), the
Securities Act of 1933, as amended (the "Securities Act") or any other federal,
state or local law regulating the Company including, without limitation, the
Company's Annual Report of Form 10-K for the fiscal year ended December 31,
1999, as prescribed by the Securities and Exchange Commission (the "Commission")
pursuant to the Act, and the rules and regulations promulgated thereunder, with
any and all exhibits and other documents relating thereto, any and all
amendments to said Annual Report and all instruments as said attorneys or any of
them shall deem necessary or incidental in connection therewith and to file the
same with the Commission.

                  Each of said attorneys shall have full power and authority to
do and perform in my name and on my behalf any act whatsoever to accomplish the
purpose and intent of the forgoing that said attorneys deem may be necessary or
desirable to be done in the premises as fully and to all intents and purposes as
I might or could do in person, and by my signature hereto, I hereby ratify and
approve any and all of such acts of said attorneys and each of them.

                  IN WITNESS WHEREOF, I have executed this instrument on this
25th day of January, 2000.



                                               /s/ W. M. BRUMLEY, JR.
                                               --------------------------------
                                               W. M. Brumley, Jr.


<PAGE>   5



                                POWER OF ATTORNEY



                  I ROBERT H. CAMPBELL, in my individual capacity and as a
director of Pogo Producing Company (the "Company"), do hereby appoint PAUL G.
VAN WAGENEN and THOMAS E. HART, and each of them severally, my true and lawful
attorney or attorneys with power to act with or without the other, and with full
power of substitution and resubstitution, to prepare, execute and file, in my
name, place and stead in my individual capacity and as a director of the
Company, such documents, reports and filings as may be necessary or advisable
under the Securities Exchange Act of 1934, as amended (the "Act"), the
Securities Act of 1933, as amended (the "Securities Act") or any other federal,
state or local law regulating the Company including, without limitation, the
Company's Annual Report of Form 10-K for the fiscal year ended December 31,
1999, as prescribed by the Securities and Exchange Commission (the "Commission")
pursuant to the Act, and the rules and regulations promulgated thereunder, with
any and all exhibits and other documents relating thereto, any and all
amendments to said Annual Report and all instruments as said attorneys or any of
them shall deem necessary or incidental in connection therewith and to file the
same with the Commission.

                  Each of said attorneys shall have full power and authority to
do and perform in my name and on my behalf any act whatsoever to accomplish the
purpose and intent of the forgoing that said attorneys deem may be necessary or
desirable to be done in the premises as fully and to all intents and purposes as
I might or could do in person, and by my signature hereto, I hereby ratify and
approve any and all of such acts of said attorneys and each of them.

                  IN WITNESS WHEREOF, I have executed this instrument on this
25th day of January, 2000.



                                               /s/ ROBERT H. CAMPBELL
                                               --------------------------------
                                               Robert H. Campbell


<PAGE>   6



                                POWER OF ATTORNEY



                  I WILLIAM L. FISHER, in my individual capacity and as a
director of Pogo Producing Company (the "Company"), do hereby appoint PAUL G.
VAN WAGENEN and THOMAS E. HART, and each of them severally, my true and lawful
attorney or attorneys with power to act with or without the other, and with full
power of substitution and resubstitution, to prepare, execute and file, in my
name, place and stead in my individual capacity and as a director of the
Company, such documents, reports and filings as may be necessary or advisable
under the Securities Exchange Act of 1934, as amended (the "Act"), the
Securities Act of 1933, as amended (the "Securities Act") or any other federal,
state or local law regulating the Company including, without limitation, the
Company's Annual Report of Form 10-K for the fiscal year ended December 31,
1999, as prescribed by the Securities and Exchange Commission (the "Commission")
pursuant to the Act, and the rules and regulations promulgated thereunder, with
any and all exhibits and other documents relating thereto, any and all
amendments to said Annual Report and all instruments as said attorneys or any of
them shall deem necessary or incidental in connection therewith and to file the
same with the Commission.

                  Each of said attorneys shall have full power and authority to
do and perform in my name and on my behalf any act whatsoever to accomplish the
purpose and intent of the forgoing that said attorneys deem may be necessary or
desirable to be done in the premises as fully and to all intents and purposes as
I might or could do in person, and by my signature hereto, I hereby ratify and
approve any and all of such acts of said attorneys and each of them.

                  IN WITNESS WHEREOF, I have executed this instrument on this 25
day of January, 2000.



                                               /s/ WILLIAM L. FISHER
                                               --------------------------------
                                               William L. Fisher


<PAGE>   7



                                POWER OF ATTORNEY



                  I GERRIT W. GONG, in my individual capacity and as a director
of Pogo Producing Company (the "Company"), do hereby appoint PAUL G. VAN WAGENEN
and THOMAS E. HART, and each of them severally, my true and lawful attorney or
attorneys with power to act with or without the other, and with full power of
substitution and resubstitution, to prepare, execute and file, in my name, place
and stead in my individual capacity and as a director of the Company, such
documents, reports and filings as may be necessary or advisable under the
Securities Exchange Act of 1934, as amended (the "Act"), the Securities Act of
1933, as amended (the "Securities Act") or any other federal, state or local law
regulating the Company including, without limitation, the Company's Annual
Report of Form 10-K for the fiscal year ended December 31, 1999, as prescribed
by the Securities and Exchange Commission (the "Commission") pursuant to the
Act, and the rules and regulations promulgated thereunder, with any and all
exhibits and other documents relating thereto, any and all amendments to said
Annual Report and all instruments as said attorneys or any of them shall deem
necessary or incidental in connection therewith and to file the same with the
Commission.

                  Each of said attorneys shall have full power and authority to
do and perform in my name and on my behalf any act whatsoever to accomplish the
purpose and intent of the forgoing that said attorneys deem may be necessary or
desirable to be done in the premises as fully and to all intents and purposes as
I might or could do in person, and by my signature hereto, I hereby ratify and
approve any and all of such acts of said attorneys and each of them.

                  IN WITNESS WHEREOF, I have executed this instrument on this 25
day of January, 2000.



                                               /s/ GERRIT W. GONG
                                               --------------------------------
                                               Gerrit W. Gong


<PAGE>   8



                                POWER OF ATTORNEY



                  I J. STUART HUNT, in my individual capacity and as a director
of Pogo Producing Company (the "Company"), do hereby appoint PAUL G. VAN WAGENEN
and THOMAS E. HART, and each of them severally, my true and lawful attorney or
attorneys with power to act with or without the other, and with full power of
substitution and resubstitution, to prepare, execute and file, in my name, place
and stead in my individual capacity and as a director of the Company, such
documents, reports and filings as may be necessary or advisable under the
Securities Exchange Act of 1934, as amended (the "Act"), the Securities Act of
1933, as amended (the "Securities Act") or any other federal, state or local law
regulating the Company including, without limitation, the Company's Annual
Report of Form 10-K for the fiscal year ended December 31, 1999, as prescribed
by the Securities and Exchange Commission (the "Commission") pursuant to the
Act, and the rules and regulations promulgated thereunder, with any and all
exhibits and other documents relating thereto, any and all amendments to said
Annual Report and all instruments as said attorneys or any of them shall deem
necessary or incidental in connection therewith and to file the same with the
Commission.

                  Each of said attorneys shall have full power and authority to
do and perform in my name and on my behalf any act whatsoever to accomplish the
purpose and intent of the forgoing that said attorneys deem may be necessary or
desirable to be done in the premises as fully and to all intents and purposes as
I might or could do in person, and by my signature hereto, I hereby ratify and
approve any and all of such acts of said attorneys and each of them.

                  IN WITNESS WHEREOF, I have executed this instrument on this
25th day of January, 2000.



                                               /s/ J. STUART HUNT
                                               --------------------------------
                                               J. Stuart Hunt


<PAGE>   9



                                POWER OF ATTORNEY



                  I FREDERICK A. KLINGENSTEIN, in my individual capacity and as
a director of Pogo Producing Company (the "Company"), do hereby appoint PAUL G.
VAN WAGENEN and THOMAS E. HART, and each of them severally, my true and lawful
attorney or attorneys with power to act with or without the other, and with full
power of substitution and resubstitution, to prepare, execute and file, in my
name, place and stead in my individual capacity and as a director of the
Company, such documents, reports and filings as may be necessary or advisable
under the Securities Exchange Act of 1934, as amended (the "Act"), the
Securities Act of 1933, as amended (the "Securities Act") or any other federal,
state or local law regulating the Company including, without limitation, the
Company's Annual Report of Form 10-K for the fiscal year ended December 31,
1999, as prescribed by the Securities and Exchange Commission (the "Commission")
pursuant to the Act, and the rules and regulations promulgated thereunder, with
any and all exhibits and other documents relating thereto, any and all
amendments to said Annual Report and all instruments as said attorneys or any of
them shall deem necessary or incidental in connection therewith and to file the
same with the Commission.

                  Each of said attorneys shall have full power and authority to
do and perform in my name and on my behalf any act whatsoever to accomplish the
purpose and intent of the forgoing that said attorneys deem may be necessary or
desirable to be done in the premises as fully and to all intents and purposes as
I might or could do in person, and by my signature hereto, I hereby ratify and
approve any and all of such acts of said attorneys and each of them.

                  IN WITNESS WHEREOF, I have executed this instrument on this
25th day of January, 2000.



                                               /s/ FREDERICK A. KLINGENSTEIN
                                               --------------------------------
                                               Frederick A. Klingenstein


<PAGE>   10



                                POWER OF ATTORNEY



                  I JACK A. VICKERS, in my individual capacity and as a director
of Pogo Producing Company (the "Company"), do hereby appoint PAUL G. VAN WAGENEN
and THOMAS E. HART, and each of them severally, my true and lawful attorney or
attorneys with power to act with or without the other, and with full power of
substitution and resubstitution, to prepare, execute and file, in my name, place
and stead in my individual capacity and as a director of the Company, such
documents, reports and filings as may be necessary or advisable under the
Securities Exchange Act of 1934, as amended (the "Act"), the Securities Act of
1933, as amended (the "Securities Act") or any other federal, state or local law
regulating the Company including, without limitation, the Company's Annual
Report of Form 10-K for the fiscal year ended December 31, 1999, as prescribed
by the Securities and Exchange Commission (the "Commission") pursuant to the
Act, and the rules and regulations promulgated thereunder, with any and all
exhibits and other documents relating thereto, any and all amendments to said
Annual Report and all instruments as said attorneys or any of them shall deem
necessary or incidental in connection therewith and to file the same with the
Commission.

                  Each of said attorneys shall have full power and authority to
do and perform in my name and on my behalf any act whatsoever to accomplish the
purpose and intent of the forgoing that said attorneys deem may be necessary or
desirable to be done in the premises as fully and to all intents and purposes as
I might or could do in person, and by my signature hereto, I hereby ratify and
approve any and all of such acts of said attorneys and each of them.

                  IN WITNESS WHEREOF, I have executed this instrument on this
25th day of January, 2000.



                                               /s/ JACK A. VICKERS
                                               --------------------------------
                                               Jack A. Vickers


<PAGE>   11



                                POWER OF ATTORNEY



                  I STEPHEN A. WELLS, in my individual capacity and as a
director of Pogo Producing Company (the "Company"), do hereby appoint PAUL G.
VAN WAGENEN and THOMAS E. HART, and each of them severally, my true and lawful
attorney or attorneys with power to act with or without the other, and with full
power of substitution and resubstitution, to prepare, execute and file, in my
name, place and stead in my individual capacity and as a director of the
Company, such documents, reports and filings as may be necessary or advisable
under the Securities Exchange Act of 1934, as amended (the "Act"), the
Securities Act of 1933, as amended (the "Securities Act") or any other federal,
state or local law regulating the Company including, without limitation, the
Company's Annual Report of Form 10-K for the fiscal year ended December 31,
1999, as prescribed by the Securities and Exchange Commission (the "Commission")
pursuant to the Act, and the rules and regulations promulgated thereunder, with
any and all exhibits and other documents relating thereto, any and all
amendments to said Annual Report and all instruments as said attorneys or any of
them shall deem necessary or incidental in connection therewith and to file the
same with the Commission.

                  Each of said attorneys shall have full power and authority to
do and perform in my name and on my behalf any act whatsoever to accomplish the
purpose and intent of the forgoing that said attorneys deem may be necessary or
desirable to be done in the premises as fully and to all intents and purposes as
I might or could do in person, and by my signature hereto, I hereby ratify and
approve any and all of such acts of said attorneys and each of them.

                  IN WITNESS WHEREOF, I have executed this instrument on this
25th day of January, 2000.



                                               /s/ STEPHEN A. WELLS
                                               --------------------------------
                                               Stephen A. Wells