SECURITIES AND EXCHANGE COMMISSION
                            Washington, D.C.  20549


                                 SCHEDULE 13D



                   Under the Securities Exchange Act of 1934


                         KLLM Transport Services, Inc.
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                                (Name of Issuer)


                    Common Stock, Par Value $1.00 Per Share
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                        (Title of Class and Securities)


                                   482498102
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                     (CUSIP Number of Class of Securities)


                  David P. Webb, Esq., Phelps Dunbar, L.L.P.
Suite 500, Mtel Centre, 200 S. Lamar Street, Jackson, MS  39201, (601) 352-2300
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           (Name, Address and Telephone Number of Person Authorized
                    to Receive Notices and Communications)


                                October 5, 1998
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            (Date of Event Which Requires Filing of this Statement)


If the filing person has previously filed a statement on Schedule 13G to report
the acquisition which is the subject of this Statement because of Rule 13D-
1(b)(3) or (4), check the following box:
[_]
Check the following box if a fee is being paid with this Statement:
[_]

 
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  CUSIP NO. 482498102                                                      13D
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      NAME OF REPORTING PERSONS
 1    S.S. OR I.R.S. IDENTIFICATION NO. OF ABOVE PERSON
      J. Tayloe Simmons, Jr., Esq.
      ###-##-####                        
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      CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP:
 2                                                              (a) [_]
                                                                (b) [_]
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      SEC USE ONLY
 3
 
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      SOURCE OF FUNDS*
 4    00-Mr. Simmons was recently appointed the executor of an estate owning
      150,000 shares and the Managing General Partner of a Partnership owning
      400,000 shares. See Item 2, below.
      
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      CHECK BOX IF DISCLOSURE OF LEGAL PROCEEDINGS IS REQUIRED PURSUANT 
      TO ITEMS 2(d) or 2(e) [_]
 5    
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      CITIZENSHIP OR PLACE OF ORGANIZATION
 6    Mississippi, U.S.A.
     
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                          SOLE VOTING POWER
                     7    150,000 shares  
     NUMBER OF            
                             
      SHARES       -----------------------------------------------------------
                          SHARED VOTING POWER
   BENEFICIALLY      8    400,000 shares
                          
     OWNED BY                    
                   -----------------------------------------------------------
       EACH               SOLE DISPOSITIVE POWER
                     9    150,000 shares 
    REPORTING             
                         
      PERSON       -----------------------------------------------------------
                          SHARED DISPOSITIVE POWER
       WITH          10   400,000 shares
                                 
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      AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON
11    550,000 shares
      
      
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      CHECK BOX IF THE AGGREGATE AMOUNT IN ROW 11 EXCLUDES CERTAIN SHARES*
12                  
      [_]
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      PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW 11
13    12.6%
                  
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      TYPE OF REPORTING PERSON*
14    IN--Individual
      
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                     *SEE INSTRUCTIONS BEFORE FILLING OUT!
        

 
Item 1.   Security and Issuer

          The class of equity securities to which this statement on Schedule 13D
relates is the common stock, par value $1.00 per share (the "Common Stock"), of
KLLM Transport Services, Inc. (the "Company"), a Delaware corporation, with
principal offices located at 135 Riverview Drive, Richland, Mississippi 39218.

Item 2.   Identity and Background

          On July 3, 1998, B. C. Lee, L.P., a Mississippi limited partnership
(the "Partnership"), was organized with Mr. Benjamin C. Lee, Jr. ("Mr. Lee"),
Mr. Benjamin Clinton Lee, III ("Mr. Lee, III") and Ms. Ruth Ann Lee Lyles ("Ms.
Lyles") as General Partners.  Mr. Lee  contributed to the capital of the
Partnership, among other things, 400,000 shares of the Company's Common Stock.
Mr. Lee passed away on August 31, 1998 and his equity interest in the
Partnership is now owned by his estate, the Estate of Benjamin C. Lee, Jr. (the
"Lee Estate"), represented by J. Tayloe Simmons, Jr., Esq., Executor ("Mr.
Simmons").  Mr. Simmons has replaced Mr. Lee as a General Partner of the
Partnership.  The Partnership was created by Mr. Lee as a family and estate
planning vehicle intended to preserve his wealth and provide for its orderly
distribution among future generations.

          The Partnership is managed by a vote of the majority in interest of
the General Partners.  The General Partners' interests in the Partnership are as
follows:  Mr. Lee, III .24%, Ms. Lyles .24% and Mr. Simmons .52%.

          The Lee Estate also owns an additional 150,000 shares of the Common
Stock which was owned by Mr. Lee at the time of his death.  Mr. Simmons is the
Executor of the Lee Estate and exercises sole voting and dispositive powers over
these shares.  When the Lee Estate is settled, which is currently anticipated
for sometime in the summer of 1999, it is anticipated that the 150,000 shares
owned by the Lee Estate will be distributed 100,000 to Mr. Lee's widow, and
50,000 shares to Mr. Lee, III and Ms. Lyles.

          The Executor of the Lee Estate is Mr. Simmons, a practicing attorney,
whose business address is 501 South State Street, Jackson, Mississippi 39201.

     d)   N/A

     e)   N/A

     f)   Mr. Simmons is a citizen of the United States.

Item 3.   Source and Amount of Funds or Other Consideration

          400,000 shares of the Common Stock were acquired by the Partnership as
a capital contribution by Mr. Lee.  Mr. Lee owned an additional 150,000 shares
at the time of his death.  See Item 2, above.

Item 4.   Purpose of Transaction

          The Common Stock was acquired by the Partnership for investment for
family and estate planning purposes.  The reporting person does not have any
plans or proposals which relate to or would result in:

 
     a)   The acquisition of additional securities of the Company, or the
disposition of securities of the Company;

     b)   An extraordinary corporate transaction, such as a merger,
reorganization or liquidation, involving the Company or any of its subsidiaries;

     c)   A sale or transfer of a material amount of assets of the Company or
any of its subsidiaries;

     d)   Any change in the present board of directors or management of the
Company, including any plans or proposals to change the number or term of
directors or to fill any existing vacancies on the board;

     e)   Any material change in the present capitalization or dividend policy
of the Company;

     f)   Any other material change in the Company's business or corporate
structure;

     g)   Changes in the Company's charter or bylaws or other actions which may
impede the acquisition of control of the Company by any person;

     h)   Causing a class of securities of the Company to be delisted from a
national securities exchange or to cease to be authorized to be quoted in an
inter-dealer quotation system of a registered national securities association;

     i)   A class of equity securities of the Company becoming eligible for
termination of registration pursuant to Section 12(g)(4) of the Securities
Exchange Act of 1934, as amended; or

     j)   Any action similar to any of those described above.

Item 5.   Interest in Securities of the Issuer

     (a) The aggregate number and percentage of shares of the Common Stock to
which this Schedule 13D relates is 550,000 shares, representing 12.6% of the
4,374,473 shares outstanding as reported by the Company on July 3, 1998.

     (b) Mr. Simmons, as Executor of the Lee Estate, has the direct power to
vote and dispose of 150,000 shares of the Common Stock.  In addition, as a
General Partner of the Partnership, Mr. Simmons shares voting and dispositive
power over an additional 400,000 shares of the Common Stock.  See Item 2, above.

     (c)  None.

     (d)  N/A

     (e)  N/A

Item 6.   Contracts, Arrangements, Understandings or
          Relationships with Respect to Securities of the Issuer

          As the controlling General Partner of the Partnership and as Executor
of the Lee Estate, Mr. Simmons has a fiduciary duty to vote the Common Stock in
the best interests of the 

 
partners of the Partnership and the beneficiaries of the Lee Estate. No other
agreements or understandings exist. See Item 2, above.

Item 7.   Material to be Filed as an Exhibit

          N/A

Signature

After reasonable inquiry and to the best of my knowledge and belief, the
undersigned certifies that the information set forth in this statement is true,
complete and correct.

Dated:         October 27, 1998.



                                      /s/ J. Tayloe Simmons, Jr., Esq.
                                      ----------------------------------
                                      J. Tayloe Simmons, Jr., Esq.