EXHIBIT (a)(1)(H) This announcement is neither an offer to purchase nor a solicitation of an offer to sell Shares (as defined below). The Offer (as defined below) is made only by the Offer to Purchase dated June 2, 2000, and the related Letter of Transmittal and is being made to all holders of Shares. Purchaser (as defined below) is not aware of any state where the making of the Offer is prohibited by administrative or judicial action pursuant to a state statute. If Purchaser becomes aware of any valid state statute prohibiting the making of the Offer, Purchaser will make a reasonable good faith effort to comply with such statute or seek to have such statute declared inapplicable to the Offer. If, after such reasonable good faith effort, Purchaser cannot comply with such statute, the Offer will not be made to (nor will tenders be accepted from or on behalf of) the holders of Shares in such state. In those jurisdictions where the securities, blue sky or other laws require the Offer to be made by a licensed broker or dealer, the Offer shall be deemed to be made on behalf of Purchaser by one or more registered brokers or dealers licensed under the laws of such jurisdiction. NOTICE OF OFFER TO PURCHASE FOR CASH ALL OUTSTANDING SHARES OF COMMON STOCK (INCLUDING THE ASSOCIATED RIGHTS TO PURCHASE PREFERRED STOCK) of KLLM TRANSPORT SERVICES, INC. at $8.05 NET PER SHARE by HIGH ROAD ACQUISITION SUBSIDIARY CORP. a corporation wholly owned by HIGH ROAD ACQUISITION CORP. High Road Acquisition Subsidiary Corp., a Delaware corporation ("Purchaser") and wholly owned by High Road Acquisition Corp., a Delaware corporation ("Parent"), is offering to purchase all of the outstanding shares of common stock, par value $1.00 per share (the "Common Stock"), of KLLM Transport Services, 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 Harris Trust and Savings Bank, as successor Rights Agent (the Common Stock and the Rights are referred to herein as the "Shares"), at $8.05 per Share, net to the seller in cash, upon the terms and subject to the conditions set forth in the Offer to Purchase, dated June 2, 2000 (the "Offer to Purchase"), and in the related Letter of Transmittal (which together with any supplements thereto collectively constitute the "Offer"). Tendering stockholders who have Shares registered in their name and who tender directly will not be charged brokerage fees or commissions or, subject to Instruction 6 of the Letter of Transmittal, stock transfer taxes on the purchase of Shares by Purchaser pursuant to the Offer. THE OFFER AND WITHDRAWAL RIGHTS WILL EXPIRE AT 12:00 MIDNIGHT, NEW YORK CITY TIME, ON JUNE 29, 2000, UNLESS THE OFFER IS EXTENDED. The Offer is conditioned upon, among other things: (1) there being validly tendered and not properly withdrawn prior to the expiration of the Offer a number of Shares that, together with the 689,123 Shares (the "Liles Shares") owned by William J. Liles, III, his wife and four trusts of which Mr. Liles is a trustee, co-trustee and/or a beneficiary, would represent at least a majority of Shares outstanding on the date of purchase on a fully diluted basis and (2) the termination or expiration of any applicable waiting period under the Hart-Scott- Rodino Antitrust Improvements Act of 1976, as amended. The Offer is also subject to certain other conditions described in Section 11 of the Offer to Purchase. The Offer is not conditioned upon Parent or Purchaser obtaining financing. The purpose of the Offer is to acquire for cash a majority of the outstanding Shares of, and ultimately the entire equity interest in, the Company. The Offer is being made pursuant to a Plan of Merger and Agreement (the "Merger Agreement") dated May 25, 2000 by and among Parent, Purchaser and the Company. The Merger Agreement provides, among other things, for the making of the Offer to Purchase, and further provides that, following the completion of the Offer, upon the terms and conditions of the Merger Agreement, and in accordance with the Delaware General Corporation Law (the "DGCL"), Purchaser will be merged with and into the Company (the "Merger"). The Company will continue as the surviving corporation after the Merger and become a wholly owned subsidiary of Parent. At the effective time of the Merger, each then outstanding Share (other than Shares held by the Company in treasury, or owned by Parent or Purchaser, or Shares, if any, that are held by stockholders who are entitled to and who properly exercise appraisal rights under Delaware law) would be converted pursuant to the terms of the Merger Agreement into the right to receive $8.05 in cash paid pursuant to the Offer, without interest. The sale of Shares pursuant to the Offer and Merger will be taxable transactions for federal income tax purposes. For purposes of the Offer, Purchaser will be deemed to have accepted for payment (and thereby purchased) Shares validly tendered and not properly withdrawn as, if and when Purchaser gives oral or written notice to Harris Trust Company of New York (the "Depositary") of its acceptance for payment of such Shares pursuant to the Offer. Upon the terms and subject to the conditions of the Offer, payment for Shares accepted for payment pursuant to the Offer will be made by deposit of the purchase price therefor with the Depositary, which will act as agent for the tendering stockholders whose Shares have been accepted for payment. Upon the deposit of funds with the Depositary for the purpose of making payment to validly tendering stockholders, Purchaser's obligation to make such payment shall be satisfied and such tendering stockholders must thereafter look solely to the Depositary for payment of the amount owed to them by reason of acceptance for payment of Shares pursuant to the Offer. In all cases, payment for Shares accepted for payment pursuant to the Offer will be made only after timely receipt by the Depositary of (a) a certificate for (or timely Book-Entry Confirmation (as defined in the Offer to Purchase) with respect to) such Shares and, if the Separation Time (as defined in the Offer to Purchase) occurs, certificates for (or a timely Book-Entry Confirmation, if available, with respect to) the associated Rights (unless Purchaser elects to make payment for such Shares pending receipt of the certificates for, or a Book-Entry Confirmation with respect to such Rights as described in the Offer to Purchase), (b) a Letter of Transmittal (as defined in the Offer to Purchase), or facsimile thereof, properly completed and duly executed, with any required signature guarantees (or, in the case of a book- entry transfer, an Agent's Message (as defined in the Offer to Purchase) in lieu of the Letter of Transmittal) and (c) any other documents required by the Letter of Transmittal. Accordingly, tendering stockholders may be paid at different times depending upon when certificates for Shares (or Rights, if applicable) or Book-Entry Confirmation with respect to Shares (or Rights, if applicable) are actually received by the Depositary. Under no circumstances will interest on the purchase price of the Shares be paid by Parent or Purchaser, regardless of any extension of the Offer or any delay in making such payment. Subject to the applicable rules and regulations of the Securities and Exchange Commission and the provisions of the Merger Agreement, Purchaser expressly reserves the right, in its sole discretion, at any time or from time to time, and regardless of whether or not any of the conditions of the Offer have been satisfied, to extend the period of time during which the Offer is open by giving oral or written notice of such extension to the Depositary and by making a public announcement thereof. During any such extension, all Shares previously tendered and not withdrawn will remain subject to the Offer, subject to the right of a tendering stockholder to withdraw such stockholder's tender of Shares. An extension, delay, termination, waiver or amendment will be followed as promptly as practicable by public announcement thereof to be made no later than 9:00 a.m. Eastern time, on the next business day after the previously scheduled Expiration Date (as defined in the Offer to Purchase). Subject to the applicable rules and regulations of the Securities and Exchange Commission, the Merger Agreement requires Purchaser to provide a subsequent offering period lasting for at least three and not more than 20 business days if all of the conditions of the Offer are satisfied or waived but the number of Shares tendered and not withdrawn, together with the Liles Shares, is less than 90% of the then outstanding Shares. Stockholders who tender Shares during a subsequent offering period will not have the right to withdraw their Shares during such subsequent offering period. Tenders of Shares pursuant to the Offer are irrevocable, except that Shares tendered pursuant to the Offer may be withdrawn at any time prior to the Expiration Date and, unless theretofore accepted for payment by Purchaser pursuant to the Offer, may also be withdrawn at any time after August 1, 2000. For a withdrawal to be effective, a written, telegraphic, telex, or facsimile transmission notice of withdrawal must be timely received by the Depositary at one of its addresses set forth on the back cover of the Offer to Purchase. Any such notice of withdrawal must specify the name of the person having tendered the Shares to be withdrawn, the number of Shares to be withdrawn and the names in which the certificate(s) evidencing the Shares to be withdrawn are registered, if different from that of the person who tendered such Shares. If Shares have been tendered pursuant to the procedures for book-entry tender as set forth in Section 3 of the Offer to Purchase any notice of withdrawal must specify the names and number of the account at the Book-Entry Facility (as defined in the Offer to Purchase) to be credited with the withdrawn Shares. If certificates for Shares to be withdrawn have been delivered or otherwise identified to the Depositary, the name of the registered holder and the serial numbers of the particular certificates evidencing the Shares to be withdrawn must also be furnished to the Depositary as aforesaid prior to the physical release of the certificates and the signature(s) on the notice of withdrawal must be guaranteed by an Eligible Institution (as defined in the Offer to Purchase), unless such Shares have been tendered for the account of any Eligible Institution. All questions as to the form and validity (including time of receipt) of any notice of withdrawal will be determined by Purchaser, in its sole discretion, which determination shall be final and binding. None of Purchaser, Parent, the Depositary, the Information Agent (as set forth below) or any other person will be under any duty to give notification of any defects or irregularities in any notice of withdrawal or incur any liability for failure to give such notification. Withdrawals of tenders of Shares may not be rescinded, and any Shares properly withdrawn will be deemed not to have been validly tendered for purposes of th Offer. However, withdrawn Shares may be retendered by following one of the procedures described in Section 3 of the Offer to Purchase at any time prior to the Expiration Date. The information required to be disclosed by paragraph (d)(1) of Rule 14d-6 of the General Rules and Regulations under the Securities Exchange Act of 1934, as amended, is contained in the Offer to Purchase and is incorporated herein by reference. The Company has provided Purchaser with the Company's stockholder list and security position listings for the purpose of, among other things, disseminating the Offer to stockholders. The Offer to Purchase and the related Letter of Transmittal will be mailed to record holders of Shares and will be furnished to brokers, banks and similar persons whose names, or the names of whose nominees, appear on the stockholder list or, if applicable, who are listed as participants in a clearing agency's security position listing for subsequent transmittal to beneficial owners of Shares. The Offer to Purchase and the Letter of Transmittal contain important information which should be read carefully before any decision is made with respect to the Offer. Questions and requests for assistance may be directed to the Information Agent at the address and telephone number set forth below. Requests for additional copies of the Offer to Purchase, the related Letter of Transmittal and other tender offer materials may be directed to the Information Agent. Such additional copies will be furnished at Purchaser's expense, Purchaser will not pay any fees or commissions to any broker or dealer or any other person (other than the Information Agent and the Depositary) for soliciting tenders of Shares pursuant to the Offer. The Information Agent For The Offer Is: GEORGESON SHAREHOLDER COMMUNICATIONS INC. 17 State Street, 10/th/ Floor New York, NY 10004 Call Toll-Free (800) 223-2064