EXHIBIT (a)(1)(E) Offer to Purchase for Cash All Outstanding Shares of Common Stock (Including the Associated Preferred Stock Purchase Rights) of KLLM Transport Services, Inc. at $7.75 Net per Share by Low Acquisition, Inc. Wholly-owned by Robert E. Low, an individual residing in Springfield, Missouri THE OFFER AND WITHDRAWAL RIGHTS WILL EXPIRE AT 12:00 MIDNIGHT, NEW YORK CITY TIME, ON TUESDAY, MAY 9, 2000, UNLESS THE OFFER IS EXTENDED. April 12, 2000 To Brokers, Dealers, Commercial Banks, Trust Companies And Other Nominees: We have been appointed by Low Acquisition, Inc., a Delaware corporation ("Purchaser"), which corporation is wholly-owned by Robert E. Low, an individual residing in Springfield, Missouri ("Parent"), to act as Information Agent in connection with Purchaser's offer to purchase all outstanding shares of common stock, par value $1.00 per share (the "Common Stock"), of KLLM Transport Service, Inc., a Delaware corporation (the "Company"), including the associated rights to purchase preferred stock (the "Rights"), issued pursuant to the Stockholder Protection Rights Agreement dated as of February 13, 1997 (the "Rights Agreement") between the Company and KeyCorp Shareholder Services, Inc. (the Common Stock and the Rights together are referred to herein as the "Shares") at $7.75 per Share, net to the seller in cash, upon the terms and subject to the conditions set forth in the Offer to Purchase dated April 12, 2000 (the "Offer to Purchase") and in the related Letter of Transmittal (which, together with any amendments or supplements thereto, constitute the "Offer") enclosed herewith. Please furnish copies of the enclosed materials to those of your clients for whose accounts you hold Shares registered in your name or in the name of your nominee. The Offer is conditioned upon, among other things, there being validly tendered and not withdrawn prior to the Expiration Date (as defined in the Offer to Purchase) that number of Shares which, when added to the Shares beneficially owned by Parent, Purchaser or any subsidiary of Parent, represents at least a majority of the Shares outstanding (on a fully diluted basis) on the date Shares are accepted for payment. The Offer is also subject to other conditions set forth in the Offer to Purchase. For your information and for forwarding to your clients for whom you hold Shares registered in your name or in the name of your nominee, we are enclosing the following documents: 1. Offer to Purchase dated April 12, 2000; 2. Letter of Transmittal for your use in accepting the Offer and tendering Shares and for the information of your clients; 3. Notice of Guaranteed Delivery to be used to accept the Offer if certificates for Shares and all other required documents cannot be delivered to the Depositary (as defined below), or if the procedures for book-entry transfer cannot be completed, by the Expiration Date (as defined in the Offer to Purchase); 4. A form of letter which may be sent to your clients for whose accounts you hold Shares registered in your name or in the name of your nominee, with space provided for obtaining such clients' instructions with regard to the Offer; (a)(1)(E)-1 5. Guidelines for Certification of Taxpayer Identification Number on Substitute Form W-9; and 6. A return envelope addressed to Wilmington Trust Company (the "Depositary"). Upon the terms and subject to the conditions of the Offer (including, if the Offer is extended or amended, the terms and conditions of any such extension or amendment), Purchaser will accept for payment and pay for Shares which are validly tendered prior to the Expiration Date and not theretofore properly withdrawn when, as and if Purchaser gives oral or written notice to the Depositary of Purchaser's acceptance of such Shares for payment pursuant to the Offer. Payment for Shares purchased pursuant to the Offer will in all cases be made only after timely receipt by the Depositary of (i) certificates for such Shares, or a Book-Entry Confirmation (as defined in the Offer to Purchase), pursuant to the procedures described in Section 3 of the Offer to Purchase, (ii) a properly completed and duly executed Letter of Transmittal (or a properly completed and manually signed facsimile thereof) or an Agent's Message (as defined in the Offer to Purchase) in connection with a book-entry transfer and (iii) all other documents required by the Letter of Transmittal. Purchaser will not pay any fees or commissions to any broker or dealer or other person (other than the Information Agent and the Depositary as described in the Offer to Purchase) for soliciting tenders of Shares pursuant to the Offer. Purchaser will, however, upon request, reimburse brokers, dealers, commercial banks and trust companies for customary mailing and handling costs incurred by them in forwarding the enclosed materials to their customers. Purchaser will pay or cause to be paid all stock transfer taxes applicable to its purchase of Shares pursuant to the Offer, subject to Instruction 6 of the Letter of Transmittal. YOUR PROMPT ACTION IS REQUESTED. WE URGE YOU TO CONTACT YOUR CLIENTS AS PROMPTLY AS POSSIBLE. PLEASE NOTE THAT THE OFFER AND WITHDRAWAL RIGHTS EXPIRE AT 12:00 MIDNIGHT, NEW YORK CITY TIME, ON TUESDAY, MAY 9, 2000, UNLESS THE OFFER IS EXTENDED. In order to take advantage of the Offer, a duly executed and properly completed Letter of Transmittal (or facsimile thereof), with any required signature guarantees, or an Agent's Message in connection with a book-entry transfer of Shares, and any other required documents, should be sent to the Depositary, and certificates representing the tendered Shares should be delivered or such Shares should be tendered by book-entry transfer, all in accordance with the Instructions set forth in the Letter of Transmittal and in the Offer to Purchase. If holders of Shares wish to tender, but it is impracticable for them to forward their certificates or other required documents or to complete the procedures for delivery by book-entry transfer prior to the expiration of the Offer, a tender may be effected by following the guaranteed delivery procedures specified in Section 3 of the Offer to Purchase. Any inquiries you may have with respect to the Offer should be addressed to, and additional copies of the enclosed materials may be obtained from, the Information Agent at its address and telephone number set forth on the back cover of the Offer to Purchase. Very truly yours, MacKenzie Partners, Inc. NOTHING CONTAINED HEREIN OR IN THE ENCLOSED DOCUMENTS SHALL CONSTITUTE YOU AS THE AGENT OF PARENT, PURCHASER, THE COMPANY, THE DEPOSITARY OR ANY AFFILIATE OF ANY OF THE FOREGOING, OR AUTHORIZE YOU OR ANY OTHER PERSON TO USE ANY DOCUMENT OR MAKE ANY STATEMENT ON BEHALF OF ANY OF THEM IN CONNECTION WITH THE OFFER OTHER THAN THE DOCUMENTS ENCLOSED HEREWITH AND THE STATEMENTS CONTAINED THEREIN. (a)(1)(E)-2