<PAGE>
 
                                                                      EXHIBIT 24

                               POWER OF ATTORNEY


KNOW ALL PERSONS BY THESE PRESENTS:

     That the undersigned, a Director of FEDERAL EXPRESS CORPORATION (the
"Corporation"), a Delaware corporation, does hereby constitute and appoint
Theodore L. Weise, Tracy G. Schmidt and Michael W. Hillard, and each of them,
with full power of substitution and resubstitution, his true and lawful
attorneys-in-fact and agents, with full power and authority to execute in the
name and on behalf of the undersigned as such Director, the Corporation's Annual
Report on Form 10-K with respect to the Corporation's fiscal year ended May 31,
1998, and any and all amendments thereto; and hereby ratifies and confirms all
that said attorneys-in-fact and agents, or any of them, or their or his
substitute or substitutes may lawfully do or cause to be done by virtue of these
presents.
 
     IN WITNESS WHEREOF, I have hereunto set my hand this 10th day of August,
1998.



                                    /s/DAVID J. BRONCZEK
                                    ----------------------------------------
                                    David J. Bronczek


STATE OF TENNESSEE

COUNTY OF SHELBY


     I, Rosemary Morlan, a Notary Public in and for said County, in the
aforesaid State, do hereby certify that David J. Bronczek, personally known to
me to be the same person whose name is subscribed to the foregoing instrument,
appeared before me this day in person, and acknowledged that he signed and
delivered the said instrument as his free and voluntary act, for the uses and
purposes therein set forth.



                                    /s/ROSEMARY MORLAN
                                    ----------------------------------------
                                    Notary Public

My Commission Expires:

 December 21, 1998
-------------------
<PAGE>
 
                               POWER OF ATTORNEY


KNOW ALL PERSONS BY THESE PRESENTS:

     That the undersigned, a Director of FEDERAL EXPRESS CORPORATION (the
"Corporation"), a Delaware corporation, does hereby constitute and appoint
Theodore L. Weise, Tracy G. Schmidt and Michael W. Hillard, and each of them,
with full power of substitution and resubstitution, his true and lawful
attorneys-in-fact and agents, with full power and authority to execute in the
name and on behalf of the undersigned as such Director, the Corporation's Annual
Report on Form 10-K with respect to the Corporation's fiscal year ended May 31,
1998, and any and all amendments thereto; and hereby ratifies and confirms all
that said attorneys-in-fact and agents, or any of them, or their or his
substitute or substitutes may lawfully do or cause to be done by virtue of these
presents.
 
     IN WITNESS WHEREOF, I have hereunto set my hand this 10th day of August,
1998.



                                    /s/T. MICHAEL GLENN
                                    ----------------------------------------
                                    T. Michael Glenn


STATE OF TENNESSEE

COUNTY OF SHELBY


     I, Joyce J. Jones, a Notary Public in and for said County, in the aforesaid
State, do hereby certify that T. Michael Glenn, personally known to me to be the
same person whose name is subscribed to the foregoing instrument, appeared
before me this day in person, and acknowledged that he signed and delivered the
said instrument as his free and voluntary act, for the uses and purposes therein
set forth.



                                    /s/JOYCE J. JONES
                                    ----------------------------------------
                                    Notary Public

My Commission Expires:

  July 9, 2002
----------------------
<PAGE>
 
                               POWER OF ATTORNEY


KNOW ALL PERSONS BY THESE PRESENTS:

     That the undersigned, a Director of FEDERAL EXPRESS CORPORATION (the
"Corporation"), a Delaware corporation, does hereby constitute and appoint
Theodore L. Weise, Tracy G. Schmidt and Michael W. Hillard, and each of them,
with full power of substitution and resubstitution, his true and lawful
attorneys-in-fact and agents, with full power and authority to execute in the
name and on behalf of the undersigned as such Director, the Corporation's Annual
Report on Form 10-K with respect to the Corporation's fiscal year ended May 31,
1998, and any and all amendments thereto; and hereby ratifies and confirms all
that said attorneys-in-fact and agents, or any of them, or their or his
substitute or substitutes may lawfully do or cause to be done by virtue of these
presents.
 
     IN WITNESS WHEREOF, I have hereunto set my hand this 10th day of August,
1998.



                                    /s/ALAN B. GRAF, JR.
                                    ----------------------------------------
                                    Alan B. Graf, Jr.


STATE OF TENNESSEE

COUNTY OF SHELBY


     I, Mary T. Britt, a Notary Public in and for said County, in the aforesaid
State, do hereby certify that Alan B. Graf, Jr., personally known to me to be
the same person whose name is subscribed to the foregoing instrument, appeared
before me this day in person, and acknowledged that he signed and delivered the
said instrument as his free and voluntary act, for the uses and purposes therein
set forth.



                                    /s/MARY T. BRITT
                                    ----------------------------------------
                                    Notary Public

My Commission Expires:

  April 14, 2001
---------------------
<PAGE>
 
                               POWER OF ATTORNEY
                                        

KNOW ALL PERSONS BY THESE PRESENTS:

     That the undersigned, a Director of FEDERAL EXPRESS CORPORATION (the
"Corporation"), a Delaware corporation, does hereby constitute and appoint
Theodore L. Weise, Tracy G. Schmidt and Michael W. Hillard, and each of them,
with full power of substitution and resubstitution, his true and lawful
attorneys-in-fact and agents, with full power and authority to execute in the
name and on behalf of the undersigned as such Director, the Corporation's Annual
Report on Form 10-K with respect to the Corporation's fiscal year ended May 31,
1998, and any and all amendments thereto; and hereby ratifies and confirms all
that said attorneys-in-fact and agents, or any of them, or their or his
substitute or substitutes may lawfully do or cause to be done by virtue of these
presents.
 
     IN WITNESS WHEREOF, I have hereunto set my hand this 10th day of August,
1998.



                                    /s/SCOTT E. HANSEN
                                    ----------------------------------------
                                    Scott E. Hansen


STATE OF TENNESSEE

COUNTY OF SHELBY


     I, Joyce J. Jones, a Notary Public in and for said County, in the aforesaid
State, do hereby certify that Scott E. Hansen, personally known to me to be the
same person whose name is subscribed to the foregoing instrument, appeared
before me this day in person, and acknowledged that he signed and delivered the
said instrument as his free and voluntary act, for the uses and purposes therein
set forth.



                                    /s/JOYCE J. JONES
                                    ----------------------------------------
                                    Notary Public

My Commission Expires:

  July 9, 2002
----------------------
<PAGE>
 
                               POWER OF ATTORNEY
                                        

KNOW ALL PERSONS BY THESE PRESENTS:

     That the undersigned, a Director of FEDERAL EXPRESS CORPORATION (the
"Corporation"), a Delaware corporation, does hereby constitute and appoint
Theodore L. Weise, Tracy G. Schmidt and Michael W. Hillard, and each of them,
with full power of substitution and resubstitution, his true and lawful
attorneys-in-fact and agents, with full power and authority to execute in the
name and on behalf of the undersigned as such Director, the Corporation's Annual
Report on Form 10-K with respect to the Corporation's fiscal year ended May 31,
1998, and any and all amendments thereto; and hereby ratifies and confirms all
that said attorneys-in-fact and agents, or any of them, or their or his
substitute or substitutes may lawfully do or cause to be done by virtue of these
presents.
 
     IN WITNESS WHEREOF, I have hereunto set my hand this 10th day of August,
1998.



                                    /s/GEORGE W. HEARN
                                    ----------------------------------------
                                    George W. Hearn


STATE OF TENNESSEE

COUNTY OF SHELBY


     I, Anne R. Coleman, a Notary Public in and for said County, in the
aforesaid State, do hereby certify that George W. Hearn, personally known to me
to be the same person whose name is subscribed to the foregoing instrument,
appeared before me this day in person, and acknowledged that he signed and
delivered the said instrument as his free and voluntary act, for the uses and
purposes therein set forth.



                                    /s/ANNE R. COLEMAN
                                    ----------------------------------------
                                    Notary Public

My Commission Expires:

 October 24, 2001
----------------------
<PAGE>
 
                               POWER OF ATTORNEY
                                        

KNOW ALL PERSONS BY THESE PRESENTS:

     That the undersigned, the principal accounting officer of FEDERAL EXPRESS
CORPORATION (the "Corporation"), a Delaware corporation, does hereby constitute
and appoint Theodore L. Weise and Tracy G. Schmidt, and each of them, with full
power of substitution and resubstitution, his true and lawful attorneys-in-fact
and agents, with full power and authority to execute in the name and on behalf
of the undersigned as such officer, the Corporation's Annual Report on Form 10-K
with respect to the Corporation's fiscal year ended May 31, 1998, and any and
all amendments thereto; and hereby ratifies and confirms all that said
attorneys-in-fact and agents, or any of them, or their or his substitute or
substitutes may lawfully do or cause to be done by virtue of these presents.
 
     IN WITNESS WHEREOF, I have hereunto set my hand this 10th day of August,
1998.



                                    /s/MICHAEL W. HILLARD
                                    ----------------------------------------
                                    Michael W. Hillard


STATE OF TENNESSEE

COUNTY OF SHELBY


     I, Delores M. Wolfmeyer, a Notary Public in and for said County, in the
aforesaid State, do hereby certify that Michael W. Hillard, personally known to
me to be the same person whose name is subscribed to the foregoing instrument,
appeared before me this day in person, and acknowledged that he signed and
delivered the said instrument as his free and voluntary act, for the uses and
purposes therein set forth.



                                    /s/DELORES M. WOLFMEYER
                                    ----------------------------------------
                                    Notary Public

My Commission Expires:

  September 26, 2000
-----------------------
<PAGE>
 
                               POWER OF ATTORNEY


KNOW ALL PERSONS BY THESE PRESENTS:

     That the undersigned, a Director of FEDERAL EXPRESS CORPORATION (the
"Corporation"), a Delaware corporation, does hereby constitute and appoint
Theodore L. Weise, Tracy G. Schmidt and Michael W. Hillard, and each of them,
with full power of substitution and resubstitution, his true and lawful
attorneys-in-fact and agents, with full power and authority to execute in the
name and on behalf of the undersigned as such Director, the Corporation's Annual
Report on Form 10-K with respect to the Corporation's fiscal year ended May 31,
1998, and any and all amendments thereto; and hereby ratifies and confirms all
that said attorneys-in-fact and agents, or any of them, or their or his
substitute or substitutes may lawfully do or cause to be done by virtue of these
presents.
 
     IN WITNESS WHEREOF, I have hereunto set my hand this 12th day of August,
1998.


                                    /s/DENNIS H. JONES
                                    ----------------------------------------
                                    Dennis H. Jones


STATE OF TENNESSEE

COUNTY OF SHELBY


     I, Mary T. Britt, a Notary Public in and for said County, in the aforesaid
State, do hereby certify that Dennis H. Jones, personally known to me to be the
same person whose name is subscribed to the foregoing instrument, appeared
before me this day in person, and acknowledged that he signed and delivered the
said instrument as his free and voluntary act, for the uses and purposes therein
set forth.



                                    /s/MARY T. BRITT
                                    ----------------------------------------
                                    Notary Public

My Commission Expires:

 April 14, 2001
----------------------
<PAGE>
 
                               POWER OF ATTORNEY
                                        

KNOW ALL PERSONS BY THESE PRESENTS:

     That the undersigned, a Director of FEDERAL EXPRESS CORPORATION (the
"Corporation"), a Delaware corporation, does hereby constitute and appoint
Theodore L. Weise, Tracy G. Schmidt and Michael W. Hillard, and each of them,
with full power of substitution and resubstitution, her true and lawful
attorneys-in-fact and agents, with full power and authority to execute in the
name and on behalf of the undersigned as such Director, the Corporation's Annual
Report on Form 10-K with respect to the Corporation's fiscal year ended May 31,
1998, and any and all amendments thereto; and hereby ratifies and confirms all
that said attorneys-in-fact and agents, or any of them, or their or his
substitute or substitutes may lawfully do or cause to be done by virtue of these
presents.
 
     IN WITNESS WHEREOF, I have hereunto set my hand this 10th day of August,
1998.



                                    /s/KENNETH R. MASTERSON
                                    ----------------------------------------
                                    Kenneth R. Masterson


STATE OF TENNESSEE

COUNTY OF SHELBY


     I, Mary T. Britt, a Notary Public in and for said County, in the aforesaid
State, do hereby certify that Kenneth R. Masterson, personally known to me to be
the same person whose name is subscribed to the foregoing instrument, appeared
before me this day in person, and acknowledged that she signed and delivered the
said instrument as her free and voluntary act, for the uses and purposes therein
set forth.



                                    /s/MARY T. BRITT
                                    ----------------------------------------
                                    Notary Public

My Commission Expires:

April 14, 2001
----------------------
<PAGE>
 
                               POWER OF ATTORNEY
                                        

KNOW ALL PERSONS BY THESE PRESENTS:

     That the undersigned, the principal financial officer of FEDERAL EXPRESS
CORPORATION (the "Corporation"), a Delaware corporation, does hereby constitute
and appoint Theodore L. Weise and Michael W. Hillard, and each of them, with
full power of substitution and resubstitution, his true and lawful attorneys-in-
fact and agents, with full power and authority to execute in the name and on
behalf of the undersigned as such officer, the Corporation's Annual Report on
Form 10-K with respect to the Corporation's fiscal year ended May 31, 1998, and
any and all amendments thereto; and hereby ratifies and confirms all that said
attorneys-in-fact and agents, or any of them, or their or his substitute or
substitutes may lawfully do or cause to be done by virtue of these presents.
 
     IN WITNESS WHEREOF, I have hereunto set my hand this 17th day of August,
1998.



                                    /s/TRACY G. SCHMIDT
                                    ----------------------------------------
                                    Tracy G. Schmidt


STATE OF TENNESSEE

COUNTY OF SHELBY


     I, Claudia Lach Hite, a Notary Public in and for said County, in the
aforesaid State, do hereby certify that Tracy G. Schmidt, personally known to me
to be the same person whose name is subscribed to the foregoing instrument,
appeared before me this day in person, and acknowledged that he signed and
delivered the said instrument as his free and voluntary act, for the uses and
purposes therein set forth.



                                    /s/CLAUDIA LACH HITE
                                    ----------------------------------------
                                    Notary Public

My Commission Expires:

 December 1, 2000
----------------------
<PAGE>
 
                               POWER OF ATTORNEY
                                        

KNOW ALL PERSONS BY THESE PRESENTS:

     That the undersigned, a Director of FEDERAL EXPRESS CORPORATION (the
"Corporation"), a Delaware corporation, does hereby constitute and appoint
Theodore L. Weise, Tracy G. Schmidt and Michael W. Hillard, and each of them,
with full power of substitution and resubstitution, his true and lawful
attorneys-in-fact and agents, with full power and authority to execute in the
name and on behalf of the undersigned as such Director, the Corporation's Annual
Report on Form 10-K with respect to the Corporation's fiscal year ended May 31,
1998, and any and all amendments thereto; and hereby ratifies and confirms all
that said attorneys-in-fact and agents, or any of them, or their or his
substitute or substitutes may lawfully do or cause to be done by virtue of these
presents.
 
     IN WITNESS WHEREOF, I have hereunto set my hand this 10th day of August
1998.



                                    /s/FREDERICK W. SMITH
                                    ----------------------------------------
                                    Frederick W. Smith


STATE OF TENNESSEE

COUNTY OF SHELBY



     I, Joyce J. Jones, a Notary Public in and for said County, in the aforesaid
State, do hereby certify that Frederick W. Smith, personally known to me to be
the same person whose name is subscribed to the foregoing instrument, appeared
before me this day in person, and acknowledged that he signed and delivered the
said instrument as his free and voluntary act, for the uses and purposes therein
set forth.


                                    /s/JOYCE J. JONES
                                    ----------------------------------------
                                    Notary Public

My Commission Expires:

     July 9, 2002
----------------------
<PAGE>
 
                               POWER OF ATTORNEY
                                        

KNOW ALL PERSONS BY THESE PRESENTS:

     That the undersigned, the principal executive officer and a director of
FEDERAL EXPRESS CORPORATION (the "Corporation"), a Delaware corporation, does
hereby constitute and appoint Tracy G. Schmidt and Michael W. Hillard, and each
of them, with full power of substitution and resubstitution, his true and lawful
attorneys-in-fact and agents, with full power and authority to execute in the
name and on behalf of the undersigned as such officer and director, the
Corporation's Annual Report on Form 10-K with respect to the Corporation's
fiscal year ended May 31, 1998, and any and all amendments thereto; and hereby
ratifies and confirms all that said attorneys-in-fact and agents, or any of
them, or their or his substitute or substitutes may lawfully do or cause to be
done by virtue of these presents.
 
     IN WITNESS WHEREOF, I have hereunto set my hand this 10th day of August,
1998.



                                    /s/THEODORE L. WEISE
                                    ----------------------------------------
                                    Theodore L. Weise


STATE OF TENNESSEE

COUNTY OF SHELBY


     I, Joyce J. Jones, a Notary Public in and for said County, in the aforesaid
State, do hereby certify that Theodore L. Weise, personally known to me to be
the same person whose name is subscribed to the foregoing instrument, appeared
before me this day in person, and acknowledged that he signed and delivered the
said instrument as his free and voluntary act, for the uses and purposes therein
set forth.



                                    /s/JOYCE J. JONES
                                    ----------------------------------------
                                    Notary Public

My Commission Expires:

    July 9, 2002
----------------------