Exhibit 32

CERTIFICATIONS OF CHIEF EXCECUTIVE OFFICER AND CHIEF FINANCIAL OFFICER

PURSUANT TO 18 U.S.C. SECTION 1350

SECTION 906 OF THE SARBANES-OXLEY ACT OF 2002

In connection with the Annual Report on Form 10-K of J.B. Hunt Transport Services, Inc. (the “Company”) for the period ended December 31, 2009, as filed with the Securities and Exchange Commission on the date hereof (the “Report’), the undersigned, in the capacities and on the dates indicated below, each 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.

Date: February 26, 2010  /s/ Kirk Thompson                                           

Kirk Thompson

President and Chief Executive Officer

Date: February 26, 2010   /s/ David G. Mee                                           

David G. Mee

Executive Vice President, Finance and

Administration, Chief Financial Officer