EXHIBIT 32

CERTIFICATION PURSUANT TO

18 U.S.C. SECTION 1350,

AS ADOPTED PURSUANT TO

SECTION 906 OF THE SARBANES-OXLEY ACT OF 2002

In connection with the Quarterly Report on Form 10-Q of Texland Drilling Program-1981, LTD, (the “Company”) for the period ended June 30, 2004 as filed with the Securities and Exchange Commission on the date hereof ( the “Report”), we, Jerry N. Namy, Chief Executive Officer of the Company, and M. E. Chapman, Chief Financial Officer of the Company, hereby certify, pursuant to 18 U.S.C. Section 1350, as adopted pursuant to Section 906 of the Sarbanes-Oxley Act of 2002, that to the best of our knowledge:

(1)

The Report fully complies with the requirements of Section 13 (a) or 15 (d) of the Securities Exchange Act of 1934, as amended; and

(2)

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


By:		/s/ Jerry N. Namy
		Jerry N. Namy
		Chief Executive Officer
		August 17, 2004

By:		/s/ M. E. Chapman
		M. E. Chapman
		Chief Financial Officer
		August 17, 2004

TEXLAND DRILLING PROGRAM 1981 10-Q