<PAGE>   1



                                  UNITED STATES
                       SECURITIES AND EXCHANGE COMMISSION

                             Washington, D. C. 20549

                                    FORM 10-Q

               QUARTERLY REPORT PURSUANT TO SECTION 13 OR 15(d) OF
                       THE SECURITIES EXCHANGE ACT OF 1934

For the Quarterly Period Ended July 2, 1999      Commission File Number 0-14759
                              -------------                             -------


                          KLLM TRANSPORT SERVICES, INC.
              ----------------------------------------------------
             (Exact name of registrant as specified in its charter)


              Delaware                                      64-0412551
              --------                                      ----------
    (State or other jurisdiction of                         (I.R.S. Employer
    incorporation or organization)                          Identification No.)

         135 Riverview Drive
         Richland, Mississippi                                  39218
         ---------------------                                  -----
 (Address of principal executive offices)                     (Zip Code)

        Registrant's telephone number, including area code  (601) 939-2545
                                                           ----------------


      Indicate by check mark whether the registrant (1) has filed all reports
required to be filed by Section 13 or 15(d) of the Securities Exchange Act of
1934 during the preceding 12 months, and (2) has been subject to such filing
requirements for the past 90 days.

                                                             Yes  [X]   No [ ]


      4,095,134 Common Shares were outstanding as of July 2, 1999.


<PAGE>   2




                          KLLM TRANSPORT SERVICES, INC.
                                AND SUBSIDIARIES

                                      INDEX

<TABLE>
<CAPTION>

                                                                            Page
                                                                           Number
                                                                           ------
<S>                                                                        <C>
PART I.  FINANCIAL INFORMATION:

  Item 1.  Financial Statements

                   Condensed Consolidated Balance Sheets
                      July 2, 1999 (Unaudited) and January 1, 1999            1

                   Consolidated Statements of Earnings (Unaudited)
                      Thirteen weeks and Twenty-six weeks ended
                      July 2, 1999 and July 3, 1998                           2

                   Condensed Consolidated Statements of Cash Flows
                     (Unaudited) Twenty-six weeks ended
                      July 2, 1999 and July 3, 1998                           3

                   Notes to Condensed Consolidated Financial
                      Statements (Unaudited)                                  4

  Item 2.  Management's Discussion and Analysis of Financial
              Condition and Results of Operations                             5

  Item 3.  Quantitative and Qualitative Disclosures about Market Risk         7

PART II.   OTHER INFORMATION:

  Item 6.  Exhibits and Reports on Form 8-K                                   8

</TABLE>


<PAGE>   3

                          KLLM TRANSPORT SERVICES, INC
                                AND SUBSIDIARIES
                      CONDENSED CONSOLIDATED BALANCE SHEETS


<TABLE>
<CAPTION>

                                                                                  July 2,          January 1,
                                                                                   1999              1999
                                                                                ----------         ----------
                                                                                (Unaudited)         (Note)
                                                                                         (In thousands)

<S>                                                                             <C>                 <C>
                                     ASSETS

Current assets:
     Cash and cash equivalents                                                    $   1,142         $     756
     Accounts receivable                                                             24,390            21,132
     Inventories - at cost                                                              771               597
     Prepaid expenses:
          Tires                                                                       2,847             2,758
          Other                                                                       3,395             2,490
     Assets held for sale                                                             1,530             1,530
     Deferred income taxes                                                            5,818             5,818
                                                                                  ---------         ---------
               Total current assets                                                  39,893            35,081

Property and equipment                                                              134,957           131,953
     Less accumulated depreciation                                                  (39,703)          (33,741)
                                                                                  ---------         ---------
                                                                                     95,254            98,212
Other assets                                                                             22                69
                                                                                  ---------         ---------
                                                                                  $ 135,169         $ 133,362
                                                                                  =========         =========

                      LIABILITIES AND STOCKHOLDERS' EQUITY

Current liabilities:
     Accounts payable and accrued expenses                                        $  13,574         $  11,745
     Accrued claims expense                                                          14,452            15,041
     Current maturities of long-term debt
       and capital leases                                                                 0             2,857
                                                                                  ---------         ---------
          Total current liabilities                                                  28,026            29,643

Long-term debt and capital leases, less
  current maturities                                                                 41,000            36,571

Deferred income taxes                                                                14,480            14,480

Stockholders' equity:
     Preferred Stock, $.01 value; authorized 5,000,000 shares; none issued
     Common Stock, $1 par value; 10,000,000 shares authorized;
       issued shares - 4,558,754 in 1999 and 1998;
       outstanding shares - 4,095,134 in 1999 and 4,224,488 in 1998                   4,559             4,559
     Additional paid-in capital                                                      32,840            32,858
     Retained earnings                                                               18,494            18,569
                                                                                  ---------         ---------
                                                                                     55,893            55,986
     Less common stock in treasury, 463,620 shares
       in 1999 and 334,266 shares in 1998, at cost                                   (4,230)           (3,318)
                                                                                  ---------         ---------
          Total stockholders' equity                                                 51,663            52,668
                                                                                  ---------         ---------
                                                                                  $ 135,169         $ 133,362
                                                                                  =========         =========

</TABLE>

Note: The balance sheet at January 1, 1999 has been derived from the audited
financial statements at the date indicated, but does not include all of the
information and footnotes required by generally accepted accounting principles
for complete financial statements.

See accompanying notes.


<PAGE>   4




                          KLLM TRANSPORT SERVICES, INC.
                                AND SUBSIDIARIES
                       CONSOLIDATED STATEMENTS OF EARNINGS
                                   (UNAUDITED)

<TABLE>
<CAPTION>


                                                                       Thirteen Weeks Ended              Twenty-Six Weeks Ended
                                                                      July 2,        July 3,            July 2,          July 3,
                                                                       1999           1998               1999             1998
                                                                    -------------------------         ---------------------------
                                                                                (IN THOUSANDS, EXCEPT PER SHARE AMOUNTS)

<S>                                                                 <C>              <C>              <C>               <C>
OPERATING REVENUE                                                   $ 61,229         $ 60,113         $ 116,560         $ 119,303

OPERATING EXPENSES:

  Salaries, wages and fringe benefits                                 21,015           18,081            40,357            37,837
  Operating supplies and expenses                                     14,970           14,514            28,116            28,845
  Insurance, claims, taxes and licenses                                2,798            3,938             5,941             7,188
  Depreciation and amortization                                        4,574            4,514             8,941             9,174
  Purchased transportation and equipment rent                         13,855           13,431            26,206            26,167
  Other                                                                2,866            2,985             5,545             5,714
  Gain on sale of revenue equipment                                     (391)            (205)             (508)             (207)
                                                                    --------         --------         ---------         ---------
    TOTAL OPERATING EXPENSES                                          59,687           57,258           114,598           114,718
                                                                    --------         --------         ---------         ---------

    OPERATING INCOME                                                   1,542            2,855             1,962             4,585

Interest and other income                                                (13)             (19)              (21)             (926)
Interest expense                                                         908              870             1,711             1,826
                                                                    --------         --------         ---------         ---------
                                                                         895              851             1,690               900
                                                                    --------         --------         ---------         ---------

EARNINGS BEFORE INCOME TAXES AND EXTRAORDINARY ITEM                      647            2,004               272             3,685
Income taxes                                                             250              800               100             1,475
                                                                    --------         --------         ---------         ---------

NET EARNINGS BEFORE EXTRAORDINARY ITEM                                   397            1,204               172             2,210

Expenses associated with the early extinguishment of debt,
   net of taxes                                                          247                0               247                 0
                                                                    ========         ========         =========         =========
NET EARNINGS (LOSS)                                                 $    150         $  1,204         $     (75)        $   2,210
                                                                    ========         ========         =========         =========


BASIC AND DILUTED EARNINGS (LOSS) PER COMMON SHARE:
    From operations                                                 $   0.10         $   0.28         $    0.04         $    0.51
    From expenses associated with the early extinguishment
       of debt                                                         (0.06)               0             (0.06)                0
                                                                    ========         ========         =========         =========
    Net earnings (loss) per common share                            $   0.04         $   0.28         $   (0.02)        $    0.51
                                                                    ========         ========         =========         =========


</TABLE>


See accompanying notes.




                                       2


<PAGE>   5


                          KLLM TRANSPORT SERVICES, INC.
                                AND SUBSIDIARIES
                 CONDENSED CONSOLIDATED STATEMENTS OF CASH FLOWS
                                   (UNAUDITED)

<TABLE>
<CAPTION>

                                                                       Twenty-Six Weeks Ended
                                                                      July 2,          July 3,
                                                                       1999             1998
                                                                     ---------         -------
                                                                            (In Thousands)

<S>                                                                   <C>              <C>
NET CASH PROVIDED BY OPERATING
     ACTIVITIES                                                       $  5,447         $ 10,241

CASH FLOWS FROM INVESTING ACTIVITIES:
   Purchases of property and equipment                                 (16,077)          (5,673)
   Proceeds from disposition of property, equipment and
      assets held for sale                                              10,404            5,014
                                                                      --------         --------
NET CASH FLOWS USED IN INVESTING ACTIVITIES                             (5,673)            (659)

CASH FLOWS FROM FINANCING ACTIVITIES:
   Purchases of common stock for treasury                                 (960)               0
   Net increase (decrease) in borrowings under
     revolving line of credit                                           13,000           (6,000)
   Repayment of long-term debt and capital leases                      (11,428)          (3,246)
                                                                      --------         --------
NET CASH FLOWS PROVIDED BY (USED IN)
     FINANCING ACTIVITIES                                                  612           (9,246)
                                                                      --------         --------

     Net Increase in Cash and Cash Equivalents                             386              336

     Cash and Cash Equivalents at Beginning of Period                      756              670
                                                                      --------         --------
     Cash and Cash Equivalents at End of Period                       $  1,142         $  1,006
                                                                      ========         ========

NONCASH FINANCING ACTIVITIES
   Common stock issued for services                                   $     30         $     17
                                                                      ========         ========

</TABLE>



See accompanying notes.


                                       3

<PAGE>   6



                          KLLM TRANSPORT SERVICES, INC
                                AND SUBSIDIARIES
              NOTES TO CONDENSED CONSOLIDATED FINANCIAL STATEMENTS
                                   (Unaudited)


      NOTE A-  BASIS OF PRESENTATION

         The accompanying unaudited condensed consolidated financial statements
have been prepared in accordance with generally accepted accounting principles
for interim financial information. They have been prepared in accordance with
the instructions to Form 10-Q and Article 10 of Regulation S-X and accordingly,
do not include all of the information and footnotes required by generally
accepted accounting principles for complete financial statements. In the opinion
of management, all adjustments (consisting of normal recurring accruals)
considered necessary for a fair presentation have been included.

         In June 1998, the FASB issued Statement of Financial Accounting
Standards No. 133, "Accounting for Derivative Instruments and Hedging
Activities" (SFAS No. 133). The provisions of SFAS No. 133 require all
derivatives to be recorded on the balance sheet at fair value. SFAS No. 133
establishes "special accounting" for fair value hedges, cash flow hedges, and
hedges of foreign currency exposures of net investments in foreign operations.
Derivatives that are not hedges must be adjusted to fair value through income.
If the derivative is a hedge, depending on the nature of the hedge, changes in
the fair value of derivatives will either be offset against the change in fair
value of the hedged item through earnings or recognized in other comprehensive
income until the hedged item is recognized in earnings. Management expects the
effect of the adoption of this statement will be insignificant to the results of
the consolidated operations and financial position of the Company when it
becomes effective for fiscal 2000.

NOTE B- FISCAL YEAR

         The Company has adopted a fiscal year-end on the Friday nearest
December 31. Accordingly, the second quarter of 1999 ended on Friday, July 2,
1999.

NOTE C- COMMITMENTS AND CONTINGENCIES

         The Company is involved in various claims and routine litigation
incidental to its business. Management is of the opinion that the outcome of
these matters will not have a material adverse effect on the consolidated
financial position or results of consolidated operations of the Company.

         To hedge its exposure to price fluctuations, the Company periodically
enters into heating oil (diesel fuel) swap agreements. Agreements to purchase
19% of the remaining 1999 anticipated fuel requirements and approximately 5% of
its anticipated fuel requirements for the year 2000 were in place at the end of
the quarter. Such agreements are settled monthly and are accounted for as hedges
with gains and losses recognized in operating expenses using the accrual method
as part of the fuel cost over the hedge period. The Company does not engage in
speculative transactions nor does the Company hold or issue derivative
instruments for trading purposes.



                                        4


<PAGE>   7



ITEM 2.  MANAGEMENT'S DISCUSSION AND ANALYSIS OF FINANCIAL CONDITION AND
         RESULTS OF OPERATIONS

RESULTS OF OPERATIONS

         Operating revenue for the second quarter of 1999 increased 2% from the
comparable period of 1998 consistent with the increase in the number of trucks
in operation. The increase in operating revenue in the second quarter consisted
of a 2% decrease from the Company's traditional over-the-road
temperature-controlled freight services, net of a 4% increase from the dry-van
over-the-road truckload division. The average revenue per mile decreased from
$1.14 to $1.12 for the second quarter of 1999 as compared to the same period in
1998. There were no fuel surcharges in either period.

         Operating revenue decreased 2% from the first six months of 1998
reflecting the impact of winter weather in the first quarter of 1999 compared to
the same period in 1998. Operating revenue in the second quarter did not dilute
the negative impact of the winter weather on 1999 revenue from the first
quarter.

         The operating ratio increased from 95.3% to 97.5% for the second
quarter of 1999 compared to the same period in 1998. During the first six months
of 1999, the operating ratio increased from 96.2% to 98.3%.

         During the third quarter of 1998, the Company implemented a
restructured pay package that increased compensation for certain drivers. An
increase in the utilization of equipment resulted in more miles which further
increased driver wages. For the first half of 1999, insurance, claims, taxes and
licenses were $1,247,000 below the first half of 1998. Favorable claims
experience combined with the results of aggressive claims management has led to
a decrease in the expense rate for insurance and claims. The Company's equipment
trade cycle resulted in a gain on the disposition of revenue equipment of
$508,000 during the first six months of 1999, an increase of $301,000 over the
same period in 1998.

         As a result of the foregoing, operating income decreased by $1,313,000
and $2,623,000 for the second quarter and first six months of 1999,
respectively, when compared to the comparable periods of 1998. For the first six
months of 1999, other income was $905,000 greater last year as a result of the
sale of the corporate office building during the first quarter of 1998.

         Net income, before the extraordinary item, decreased $807,000 and
$2,038,000 for the second quarter and the first six months of 1999,
respectively, compared to the same periods in 1998. Basic and diluted earnings
per share before the extraordinary item, decreased from $.28 to $.10 in the
second quarter of 1999 and decreased from $.51 to $.04 for the first half of
1999 compared to the same periods in 1998.

LIQUIDITY AND CAPITAL RESOURCES

         The Company's primary sources of liquidity are cash flow from
operations and its existing credit agreements. During the twenty-six weeks ended
July 2, 1999, the Company generated $5,447,000 in net cash from operating
activities.

         During the first six months of 1999, net capital resources required by
the Company were approximately $5.7 million. Net capital expenditures for the
remainder of 1999, primarily for revenue equipment, are expected to be
approximately $13 million, although management may finance a portion of the
capital expenditures with operating leases. The Company entered into operating
leases for 200 trailers during the first quarter and 400 trailers in the second
quarter of 1999. Leases for 65 tractors were also entered into during the second
quarter of 1999.

         The Company has a $50,000,000 unsecured revolving line of credit (the
"Revolver") with a syndication of banks. Borrowings under the Revolver of
$41,000,000 were outstanding at July 2, 1999. Under the terms of the Revolver,
borrowings bear interest at (i) the higher of prime rate or a rate based upon
the Federal Funds Effective Rate, (ii) a rate based upon the Eurodollar rates,
or (iii) an absolute interest rate as determined by each lender in the
syndication under a competitive bid process at the Company's option. Facilities
fees from 1/5% to 3/8% per annum are charged on the unused portion of this line.
At July 2, 1999, borrowing under the Revolver was the Company's only long-term
debt outstanding. Subsequent to the end of the quarter, the Revolver was
amended, increasing the line of credit to $60,000,000 and extending the maturity
date to April 2001.

         During the quarter, the Company fully prepaid the 9.11% senior notes
(1992 debt) which were due June 2002. Under the terms of the prepayment, fees
and other expenses totaling $247,000, net of a $150,000 tax benefit, were
incurred. With the prepayment of the 1992 debt, the Company's average effective
interest rate for debt outstanding was


                                        5


<PAGE>   8

reduced from 6.8% to 6.0%. Expenses relating to the prepayment of the 1992 debt
are included in the consolidated statements of earnings as an extraordinary
item. Prepayment of the 1992 debt eliminated certain restrictive financial
covenants.

         Working capital needs have generally been met from net cash provided
from operating activities. The Company has a $4 million unsecured working
capital line of credit with a bank, all of which was available at July 2, 1999.
Interest is at a rate based upon the Eurodollar rates with facility fees at 1/4%
per annum on the unused portion of the line.

         In 1998, the Company announced plans to purchase up to 150,000 shares
of the Company's outstanding stock. During 1999, 134,000 shares were repurchased
for $960,000 of which 50,000 shares for $356,000 were repurchased from the
Estate of B.C. Lee, Jr., former Chairman of the Board.

         The Company anticipates that its existing credit facilities along with
cash flow from operations will be sufficient to fund operating expenses, capital
expenditures, debt service, and any additional stock repurchases.

IMPACT OF YEAR 2000

         Some of the Company's older computer programs were written using two
digits rather than four to define the applicable year. As a result, those
computer programs have time-sensitive software that recognizes a date using "00"
as the year 1900 rather than the year 2000. This date problem could cause a
system failure or could cause miscalculations which would disrupt operations,
including, among other things, a temporary inability to process transactions,
send invoices, or engage in similar normal business activities. During 1999 the
Company has progressed with modifications to its computer software which will
enable its computer systems to function properly with respect to dates in the
year 2000 and thereafter. The failure of the Company, its suppliers, or its
customers to adequately prepare for the Year 2000 problem could have an adverse
effect on the consolidated operations of the Company.

         Beginning in mid 1996, the Company established a conversion timeline.
Each software system was identified and categorized as year 2000 ready,
not-ready and conversion planned, and not-ready with replacement planned. During
the two and one-half years since that study, the conversion effort and timeline
has been updated to reflect progress on the overall project. Consistent with the
original year 2000 conversion timeline, the project is approximately ninety-five
percent complete. At present, management of the Company believes that sufficient
resources are in place to complete the effort by the end of the third quarter.
Upon completion of the effort, detail testing, including actually changing the
date to the year 2000 in certain systems, will be performed to ensure a seamless
passage into the year 2000. The total project is estimated at approximately
$700,000 for the purchase of new software and the modification of existing
software with $400,000 of the total capitalized and the remaining $300,000
expensed as incurred. Through July 2, 1999, approximately $350,000 had been
capitalized and $220,000 had been expensed.

         To determine the scope of the effort beyond the Company's systems, each
operating department of the Company is determining the population of significant
suppliers and their level of preparedness. In certain applications, tests have
been performed to ensure an uneventful continuation of business. The Company's
suppliers, vendors, and equipment manufacturers, have indicated that they
continue to assess the impact of the Year 2000 on their operations. In the event
of an unforeseen problem, the Company is studying contingency plans that may
include communication with drivers other than via satellite and manual
transactions. If certain suppliers such as fuel vendors are unable to supply
products or if customer locations are closed due to their inability to operate,
the Company's operations could be suspended. Although management has been
assured that revenue equipment will not be affected, a Year 2000 electronic
malfunction could render certain equipment inoperable.

         The Company's diverse customer base provides assurance that the
inability of one customer to operate, due to Year 2000 related problems, will
not have a significant adverse impact on the operations of the Company.

FACTORS AFFECTING FUTURE PERFORMANCE

         The Company's future operating results may be affected by various
trends and factors which are beyond the Company's control. These include adverse
changes in demand for trucking services, availability of drivers and fuel
prices. Accordingly, past performance should not be presumed to be an accurate
indication of future performance.



                                        6
<PAGE>   9




SEASONALITY

         In the transportation industry, results of operations generally show a
seasonal pattern because customers reduce shipments during and after the winter
holiday season with its attendant weather variations. The Company's operating
expenses have historically been higher in the winter months primarily due to
decreased fuel efficiency and increased maintenance costs in colder weather.

FORWARD LOOKING INFORMATION

         The foregoing statements contain forward-looking statements which
involve risks and uncertainties and the Company's actual experience may differ
materially from that discussed above. Factors that may cause such a difference
include, but are not limited to, those discussed in "Factors Affecting Future
Performance" as well as future events that have the effect of reducing the
Company's available cash balances, such as unanticipated operating losses or
capital expenditures related to possible future acquisitions. Readers are
cautioned not to place undue reliance on forward-looking statements, which
reflect management's analysis only as of the date hereof. The Company assumes no
obligation to update forward-looking statements.

ITEM 3.  QUANTITATIVE AND QUALITATIVE DISCLOSURES ABOUT MARKET RISK

MARKET RISK

         Market risk relating to the Company's operations result primarily from
changes in interest rates and the price of heating oil (diesel fuel), as well as
credit risk concentration. The Company does not use financial instruments for
trading purposes and is not a party to any leveraged derivatives.

         The Company's interest expense is sensitive to changes in the general
level of U. S. interest rates.



                                        7


<PAGE>   10



PART II:  OTHER INFORMATION

Item 6.  Exhibits and Reports on Form 8-K

         Exhibit 27 - Financial Data Schedule

         There were no Form 8-K filings for the quarter ended July 2, 1999.




                                        8


<PAGE>   11


SIGNATURES

Pursuant to the requirements of the Securities Exchange Act of 1934, the
registrant has duly caused this report to be signed on its behalf by the
undersigned thereunto duly authorized.



                                          KLLM TRANSPORT SERVICES, INC.
                                          -----------------------------
                                                   (Registrant)


Date      August 16, 1999                 /s/  Jack Liles
     ---------------------------          -------------------------------------
                                          Jack Liles
                                          Chairman of the Board, President and
                                          Chief Executive Officer



Date      August 16, 1999                 /s/ Steven L. Dutro
     --------------------------           -------------------------------------
                                          Steven L. Dutro
                                          Senior Vice President and Chief
                                          Financial Officer






                                       9