FORM 4 Check this box if no longer subject to Section 16. Form 4 or Form 5 obligations may continue. See Instruction 1(b).

UNITED STATES SECURITIES AND EXCHANGE COMMISSION Washington, D.C. 20549 STATEMENT OF CHANGES IN BENEFICIAL OWNERSHIP OF SECURITIES Filed pursuant to Section 16(a) of the Securities Exchange Act of 1934, Section 17(a) of the Public Utility Holding Company Act of 1935 or Section 30(h) of the Investment Company Act of 1940

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1. Name and Address of Reporting Person * PALMER KAY J   2. Issuer Name and Ticker or Trading Symbol HUNT J B TRANSPORT SERVICES INC [JBHT] 5. Relationship of Reporting Person(s) to Issuer (Check all applicable) _____ Director _____ 10% Owner _____ Officer (give title below) __X__ Other (specify below) EVP, Chief Information Officer (Last) (First) (Middle) 615 J.B. HUNT CORPORATE DRIVE 3. Date of Earliest Transaction (Month/Day/Year) 06/02/2008 (Street) LOWELL, AR 72745 4. If Amendment, Date Original Filed(Month/Day/Year) 6. Individual or Joint/Group Filing(Check Applicable Line) _X_ Form filed by One Reporting Person ___ Form filed by More than One Reporting Person (City) (State) (Zip) Table I - Non-Derivative Securities Acquired, Disposed of, or Beneficially Owned

1.Title of Security (Instr. 3) 2. Transaction Date (Month/Day/Year) 2A. Deemed Execution Date, if any (Month/Day/Year) 3. Transaction Code (Instr. 8) 4. Securities Acquired (A) or Disposed of (D) (Instr. 3, 4 and 5) 5. Amount of Securities Beneficially Owned Following Reported Transaction(s) (Instr. 3 and 4) 6. Ownership Form: Direct (D) or Indirect (I) (Instr. 4) 7. Nature of Indirect Beneficial Ownership (Instr. 4) Code V Amount (A) or (D) Price Common Stock 06/02/2008 06/02/2008 M   2,400 A $ 3.125 36,096 D   Common Stock 06/02/2008 06/02/2008 M   12,000 A $ 5.65 48,096 D   Common Stock 06/02/2008 06/02/2008 M   6,666 A $ 7.08 54,762 D   Common Stock 06/02/2008 06/02/2008 S   3,845 D $ 34 50,917 D   Common Stock 06/02/2008 06/02/2008 S   6,741 D $ 34 44,176 D   Common Stock 06/02/2008 06/02/2008 S   1,254 D $ 34 42,922 D   Common Stock 401(k)               12,616 D

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Table II - Derivative Securities Acquired, Disposed of, or Beneficially Owned
(e.g., puts, calls, warrants, options, convertible securities)

1. Title of Derivative Security (Instr. 3)

2. Conversion or Exercise Price of Derivative Security

3. Transaction Date (Month/Day/Year)

3A. Deemed Execution Date, if any (Month/Day/Year)

4. Transaction Code (Instr. 8)

5. Number of Derivative Securities Acquired (A) or Disposed of (D) (Instr. 3, 4, and 5)

6. Date Exercisable and Expiration Date (Month/Day/Year)

7. Title and Amount of Underlying Securities (Instr. 3 and 4)

8. Price of Derivative Security (Instr. 5)

9. Number of Derivative Securities Beneficially Owned Following Reported Transaction(s) (Instr. 4)

10. Ownership Form of Derivative Security: Direct (D) or Indirect (I) (Instr. 4)

11. Nature of Indirect Beneficial Ownership (Instr. 4)

Code

V

(A)

(D)

Date Exercisable

Expiration Date

Title

Amount or Number of Shares

Restricted Stock

$ 0

07/15/2011

08/15/2015

Common Stock

44,000

44,000

D

Right to Buy Stock Option

$ 12.2

06/01/2009

10/23/2014

Common Stock

40,000

40,000

D

Right to Buy Stock Option

$ 20.365

06/01/2012

10/21/2015

Common Stock

40,000

40,000

D

Right to Buy Stock Option

$ 3.125

06/02/2008

06/02/2008

M

2,400

06/01/1999

10/08/2009

Common Stock

2,400

$ 3.125

0

D

Right to Buy Stock Option

$ 5.65

06/02/2008

06/02/2008

M

12,000

06/01/2002

02/19/2013

Common Stock

12,000

$ 5.65

36,000

D

Right to Buy Stock Option

$ 7.08

06/02/2008

06/02/2008

M

6,666

06/01/2004

10/24/2013

Common Stock

6,666

$ 7.08

26,670

D

Reporting Owners

Reporting Owner Name / Address	Relationships
	Director	10% Owner	Officer	Other
PALMER KAY J 615 J.B. HUNT CORPORATE DRIVE LOWELL, AR 72745				EVP, Chief Information Officer

Signatures

Debbie Willbanks		06/03/2008
**Signature of Reporting Person		Date

Explanation of Responses:

*	If the form is filed by more than one reporting person, see Instruction 4(b)(v).
**	Intentional misstatements or omissions of facts constitute Federal Criminal Violations. See 18 U.S.C. 1001 and 15 U.S.C. 78ff(a).

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