<PAGE>   1
                                   Exhibit 24



                                POWER OF ATTORNEY


         KNOW ALL MEN BY THESE PRESENTS, that the undersigned constitutes and
appoints Douglas C. Yearley, Ramiro G. Peru and Robert C. Swan and each of them
his true and lawful attorney-in-fact and agent, with full power of substitution
and resubstitution, for him and in his name, place and stead, in any and all
capacities:

Annual Report For the Year Ended December 31, 1999 of Phelps Dodge Corporation
on Form 10-K

                  (1) to sign the Annual Report for the fiscal year ended
         December 31, 1999 of Phelps Dodge Corporation on Form 10-K ("1999 Form
         10-K") to be filed under the Securities Exchange Act of 1934, as
         amended, and any and all amendments to such 1999 Form 10-K;

                  (2) to file such 1999 Form 10-K (and any and all such
         amendments) with all exhibits thereto, and other documents in
         connection therewith, with the Securities and Exchange Commission; and

                  (3) to take such other action as may be deemed necessary or
         appropriate in connection with such 1999 Form 10-K;

as fully to all intents and purposes as he might or could do in person, hereby
ratifying and confirming all that said attorneys-in-fact and agents of any of
them, or their or his substitute or substitutes, may lawfully do or cause to be
done by virtue hereof.

         IN WITNESS WHEREOF, the undersigned has executed this Power of Attorney
this 18th day of November, 1999.


                                        /s/ Robert N. Burt
                                        ------------------------------
                                        Robert N. Burt
<PAGE>   2
                                POWER OF ATTORNEY


         KNOW ALL MEN BY THESE PRESENTS, that the undersigned constitutes and
appoints Douglas C. Yearley, Ramiro G. Peru and Robert C. Swan and each of them
his true and lawful attorney-in-fact and agent, with full power of substitution
and resubstitution, for him and in his name, place and stead, in any and all
capacities:

Annual Report For the Year Ended December 31, 1999 of Phelps Dodge Corporation
on Form 10-K

                  (1) to sign the Annual Report for the fiscal year ended
         December 31, 1999 of Phelps Dodge Corporation on Form 10-K ("1999 Form
         10-K") to be filed under the Securities Exchange Act of 1934, as
         amended, and any and all amendments to such 1999 Form 10-K;

                  (2) to file such 1999 Form 10-K (and any and all such
         amendments) with all exhibits thereto, and other documents in
         connection therewith, with the Securities and Exchange Commission; and

                  (3) to take such other action as may be deemed necessary or
         appropriate in connection with such 1999 Form 10-K;

as fully to all intents and purposes as he might or could do in person, hereby
ratifying and confirming all that said attorneys-in-fact and agents of any of
them, or their or his substitute or substitutes, may lawfully do or cause to be
done by virtue hereof.

         IN WITNESS WHEREOF, the undersigned has executed this Power of Attorney
this 18th day of November, 1999.


                                        /s/ Archie W. Dunham
                                        ------------------------------
                                        Archie W. Dunham
<PAGE>   3
                                POWER OF ATTORNEY


         KNOW ALL MEN BY THESE PRESENTS, that the undersigned constitutes and
appoints Douglas C. Yearley, Ramiro G. Peru and Robert C. Swan and each of them
his true and lawful attorney-in-fact and agent, with full power of substitution
and resubstitution, for him and in his name, place and stead, in any and all
capacities:

Annual Report For the Year Ended December 31, 1999 of Phelps Dodge Corporation
on Form 10-K

                  (1) to sign the Annual Report for the fiscal year ended
         December 31, 1999 of Phelps Dodge Corporation on Form 10-K ("1999 Form
         10-K") to be filed under the Securities Exchange Act of 1934, as
         amended, and any and all amendments to such 1999 Form 10-K;

                  (2) to file such 1999 Form 10-K (and any and all such
         amendments) with all exhibits thereto, and other documents in
         connection therewith, with the Securities and Exchange Commission; and

                  (3) to take such other action as may be deemed necessary or
         appropriate in connection with such 1999 Form 10-K;

as fully to all intents and purposes as he might or could do in person, hereby
ratifying and confirming all that said attorneys-in-fact and agents of any of
them, or their or his substitute or substitutes, may lawfully do or cause to be
done by virtue hereof.

         IN WITNESS WHEREOF, the undersigned has executed this Power of Attorney
this 19th day of November, 1999.


                                        /s/ William A. Franke
                                        ------------------------------
                                        William A. Franke
<PAGE>   4
                                POWER OF ATTORNEY


         KNOW ALL MEN BY THESE PRESENTS, that the undersigned constitutes and
appoints Douglas C. Yearley, Ramiro G. Peru and Robert C. Swan and each of them
his true and lawful attorney-in-fact and agent, with full power of substitution
and resubstitution, for him and in his name, place and stead, in any and all
capacities:

Annual Report For the Year Ended December 31, 1999 of Phelps Dodge Corporation
on Form 10-K

                  (1) to sign the Annual Report for the fiscal year ended
         December 31, 1999 of Phelps Dodge Corporation on Form 10-K ("1999 Form
         10-K") to be filed under the Securities Exchange Act of 1934, as
         amended, and any and all amendments to such 1999 Form 10-K;

                  (2) to file such 1999 Form 10-K (and any and all such
         amendments) with all exhibits thereto, and other documents in
         connection therewith, with the Securities and Exchange Commission; and

                  (3) to take such other action as may be deemed necessary or
         appropriate in connection with such 1999 Form 10-K;

as fully to all intents and purposes as he might or could do in person, hereby
ratifying and confirming all that said attorneys-in-fact and agents of any of
them, or their or his substitute or substitutes, may lawfully do or cause to be
done by virtue hereof.

         IN WITNESS WHEREOF, the undersigned has executed this Power of Attorney
this 19th day of November, 1999.


                                        /s/ Paul Hazen
                                        ------------------------------
                                        Paul Hazen
<PAGE>   5
                                POWER OF ATTORNEY


         KNOW ALL MEN BY THESE PRESENTS, that the undersigned constitutes and
appoints Douglas C. Yearley, Ramiro G. Peru and Robert C. Swan and each of them
his true and lawful attorney-in-fact and agent, with full power of substitution
and resubstitution, for him and in his name, place and stead, in any and all
capacities:

Annual Report For the Year Ended December 31, 1999 of Phelps Dodge Corporation
on Form 10-K

                  (1) to sign the Annual Report for the fiscal year ended
         December 31, 1999 of Phelps Dodge Corporation on Form 10-K ("1999 Form
         10-K") to be filed under the Securities Exchange Act of 1934, as
         amended, and any and all amendments to such 1999 Form 10-K;

                  (2) to file such 1999 Form 10-K (and any and all such
         amendments) with all exhibits thereto, and other documents in
         connection therewith, with the Securities and Exchange Commission; and

                  (3) to take such other action as may be deemed necessary or
         appropriate in connection with such 1999 Form 10-K;

as fully to all intents and purposes as he might or could do in person, hereby
ratifying and confirming all that said attorneys-in-fact and agents of any of
them, or their or his substitute or substitutes, may lawfully do or cause to be
done by virtue hereof.

         IN WITNESS WHEREOF, the undersigned has executed this Power of Attorney
this 18th day of November, 1999.


                                        /s/ Manuel J. Iraola
                                        ------------------------------
                                        Manuel J. Iraola
<PAGE>   6
                                POWER OF ATTORNEY


         KNOW ALL MEN BY THESE PRESENTS, that the undersigned constitutes and
appoints Douglas C. Yearley, Ramiro G. Peru and Robert C. Swan and each of them
his true and lawful attorney-in-fact and agent, with full power of substitution
and resubstitution, for him and in his name, place and stead, in any and all
capacities:

Annual Report For the Year Ended December 31, 1999 of Phelps Dodge Corporation
on Form 10-K

                  (1) to sign the Annual Report for the fiscal year ended
         December 31, 1999 of Phelps Dodge Corporation on Form 10-K ("1999 Form
         10-K") to be filed under the Securities Exchange Act of 1934, as
         amended, and any and all amendments to such 1999 Form 10-K;

                  (2) to file such 1999 Form 10-K (and any and all such
         amendments) with all exhibits thereto, and other documents in
         connection therewith, with the Securities and Exchange Commission; and

                  (3) to take such other action as may be deemed necessary or
         appropriate in connection with such 1999 Form 10-K;

as fully to all intents and purposes as she might or could do in person, hereby
ratifying and confirming all that said attorneys-in-fact and agents of any of
them, or their or her substitute or substitutes, may lawfully do or cause to be
done by virtue hereof.

         IN WITNESS WHEREOF, the undersigned has executed this Power of Attorney
this 22nd day of November, 1999.


                                        /s/ Marie L. Knowles
                                        ------------------------------
                                        Marie L. Knowles
<PAGE>   7
                                POWER OF ATTORNEY


         KNOW ALL MEN BY THESE PRESENTS, that the undersigned constitutes and
appoints Douglas C. Yearley, Ramiro G. Peru and Robert C. Swan and each of them
his true and lawful attorney-in-fact and agent, with full power of substitution
and resubstitution, for him and in his name, place and stead, in any and all
capacities:

Annual Report For the Year Ended December 31, 1999 of Phelps Dodge Corporation
on Form 10-K

                  (1) to sign the Annual Report for the fiscal year ended
         December 31, 1999 of Phelps Dodge Corporation on Form 10-K ("1999 Form
         10-K") to be filed under the Securities Exchange Act of 1934, as
         amended, and any and all amendments to such 1999 Form 10-K;

                  (2) to file such 1999 Form 10-K (and any and all such
         amendments) with all exhibits thereto, and other documents in
         connection therewith, with the Securities and Exchange Commission; and

                  (3) to take such other action as may be deemed necessary or
         appropriate in connection with such 1999 Form 10-K;

as fully to all intents and purposes as he might or could do in person, hereby
ratifying and confirming all that said attorneys-in-fact and agents of any of
them, or their or his substitute or substitutes, may lawfully do or cause to be
done by virtue hereof.

         IN WITNESS WHEREOF, the undersigned has executed this Power of Attorney
this 18th day of November, 1999.


                                        /s/ Robert D. Krebs
                                        ------------------------------
                                        Robert D. Krebs
<PAGE>   8
                                POWER OF ATTORNEY


         KNOW ALL MEN BY THESE PRESENTS, that the undersigned constitutes and
appoints Douglas C. Yearley, Ramiro G. Peru and Robert C. Swan and each of them
his true and lawful attorney-in-fact and agent, with full power of substitution
and resubstitution, for him and in his name, place and stead, in any and all
capacities:

Annual Report For the Year Ended December 31, 1999 of Phelps Dodge Corporation
on Form 10-K

                  (1) to sign the Annual Report for the fiscal year ended
         December 31, 1999 of Phelps Dodge Corporation on Form 10-K ("1999 Form
         10-K") to be filed under the Securities Exchange Act of 1934, as
         amended, and any and all amendments to such 1999 Form 10-K;

                  (2) to file such 1999 Form 10-K (and any and all such
         amendments) with all exhibits thereto, and other documents in
         connection therewith, with the Securities and Exchange Commission; and

                  (3) to take such other action as may be deemed necessary or
         appropriate in connection with such 1999 Form 10-K;

as fully to all intents and purposes as he might or could do in person, hereby
ratifying and confirming all that said attorneys-in-fact and agents of any of
them, or their or his substitute or substitutes, may lawfully do or cause to be
done by virtue hereof.

         IN WITNESS WHEREOF, the undersigned has executed this Power of Attorney
this 1st day of December, 1999.


                                        /s/ Southwood J. Morcott
                                        ------------------------------
                                        Southwood J. Morcott
<PAGE>   9
                                POWER OF ATTORNEY


         KNOW ALL MEN BY THESE PRESENTS, that the undersigned constitutes and
appoints Douglas C. Yearley, Ramiro G. Peru and Robert C. Swan and each of them
his true and lawful attorney-in-fact and agent, with full power of substitution
and resubstitution, for him and in his name, place and stead, in any and all
capacities:

Annual Report For the Year Ended December 31, 1999 of Phelps Dodge Corporation
on Form 10-K

                  (1) to sign the Annual Report for the fiscal year ended
         December 31, 1999 of Phelps Dodge Corporation on Form 10-K ("1999 Form
         10-K") to be filed under the Securities Exchange Act of 1934, as
         amended, and any and all amendments to such 1999 Form 10-K;

                  (2) to file such 1999 Form 10-K (and any and all such
         amendments) with all exhibits thereto, and other documents in
         connection therewith, with the Securities and Exchange Commission; and

                  (3) to take such other action as may be deemed necessary or
         appropriate in connection with such 1999 Form 10-K;

as fully to all intents and purposes as he might or could do in person, hereby
ratifying and confirming all that said attorneys-in-fact and agents of any of
them, or their or his substitute or substitutes, may lawfully do or cause to be
done by virtue hereof.

         IN WITNESS WHEREOF, the undersigned has executed this Power of Attorney
this 1st day of December, 1999.


                                        /s/ Gordon R. Parker
                                        ------------------------------
                                        Gordon R. Parker
<PAGE>   10
                                POWER OF ATTORNEY


         KNOW ALL MEN BY THESE PRESENTS, that the undersigned constitutes and
appoints Douglas C. Yearley, Ramiro G. Peru and Robert C. Swan and each of them
his true and lawful attorney-in-fact and agent, with full power of substitution
and resubstitution, for him and in his name, place and stead, in any and all
capacities:

Annual Report For the Year Ended December 31, 1999 of Phelps Dodge Corporation
on Form 10-K

                  (1) to sign the Annual Report for the fiscal year ended
         December 31, 1999 of Phelps Dodge Corporation on Form 10-K ("1999 Form
         10-K") to be filed under the Securities Exchange Act of 1934, as
         amended, and any and all amendments to such 1999 Form 10-K;

                  (2) to file such 1999 Form 10-K (and any and all such
         amendments) with all exhibits thereto, and other documents in
         connection therewith, with the Securities and Exchange Commission; and

                  (3) to take such other action as may be deemed necessary or
         appropriate in connection with such 1999 Form 10-K;

as fully to all intents and purposes as he might or could do in person, hereby
ratifying and confirming all that said attorneys-in-fact and agents of any of
them, or their or his substitute or substitutes, may lawfully do or cause to be
done by virtue hereof.

         IN WITNESS WHEREOF, the undersigned has executed this Power of Attorney
this 18th day of November, 1999.


                                        /s/ J. Steven Whisler
                                        ------------------------------
                                        J. Steven Whisler
<PAGE>   11
                                POWER OF ATTORNEY


         KNOW ALL MEN BY THESE PRESENTS, that the undersigned constitutes and
appoints Douglas C. Yearley, Ramiro G. Peru and Robert C. Swan and each of them
his true and lawful attorney-in-fact and agent, with full power of substitution
and resubstitution, for him and in his name, place and stead, in any and all
capacities:

Annual Report For the Year Ended December 31, 1999 of Phelps Dodge Corporation
on Form 10-K

                  (1) to sign the Annual Report for the fiscal year ended
         December 31, 1999 of Phelps Dodge Corporation on Form 10-K ("1999 Form
         10-K") to be filed under the Securities Exchange Act of 1934, as
         amended, and any and all amendments to such 1999 Form 10-K;

                  (2) to file such 1999 Form 10-K (and any and all such
         amendments) with all exhibits thereto, and other documents in
         connection therewith, with the Securities and Exchange Commission; and

                  (3) to take such other action as may be deemed necessary or
         appropriate in connection with such 1999 Form 10-K;

as fully to all intents and purposes as he might or could do in person, hereby
ratifying and confirming all that said attorneys-in-fact and agents of any of
them, or their or his substitute or substitutes, may lawfully do or cause to be
done by virtue hereof.

         IN WITNESS WHEREOF, the undersigned has executed this Power of Attorney
this 18th day of November, 1999.


                                        /s/ Douglas C. Yearley
                                        ------------------------------
                                        Douglas C. Yearley