El Paso Electric 10-K 2003 FY Annual report

Exhibit 32.01

March 15, 2004

The certification set forth below is being submitted in connection with the Annual Report on Form 10-K for the fiscal year ended December 31, 2003 (the “Report”) of El Paso Electric Company (the “Company”) for the purpose of complying with Rule 13a-14(b) or Rule 15d-14(b) of the Securities Exchange Act of 1934 (the “Exchange Act”) and Section 1350 of Chapter 63 of Title 18 of the United States Code.

Gary R. Hedrick, the President and Chief Executive Officer and Terry Bassham, the Executive Vice President, Chief Financial and Administrative Officer of the Company, each certifies that, to the best of his knowledge:

1. such Report fully complies with the requirements of Section 13(a) of the Exchange Act; and

2. the information contained in the Report fairly presents, in all material respects, the financial condition and results of operations of the Company.

/s/    GARY R. HEDRICK        

Gary R. Hedrick

President and Chief Executive

Officer

/s/    TERRY BASSHAM        

Terry Bassham

Executive Vice President, Chief

Financial and Administrative Officer