<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 October 1, 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 [ ]


         4,096,834 Common Shares were outstanding as of October 1, 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
            October 1, 1999 (Unaudited) and January 1, 1999                                         1

         Consolidated Statements of Earnings (Unaudited)
            Thirteen weeks and Thirty-nine weeks ended October 1, 1999 and
            October 2, 1998                                                                         2

         Condensed Consolidated Statements of Cash Flows (Unaudited)
            Thirty-nine weeks ended October 1, 1999 and October 2, 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>
                                                                     October 1,   January 1,
                                                                        1999         1999
                                                                      ---------    ---------
                                                                     (Unaudited)    (Note)
                                                                          (In thousands)
<S>                                                                   <C>          <C>
                                     ASSETS
Current assets:
     Cash and cash equivalents                                        $     434    $     756
     Accounts receivable                                                 24,849       21,132
     Inventories - at cost                                                  652          597
     Prepaid expenses:
          Tires                                                           3,285        2,758
          Other                                                           2,716        2,490
     Assets held for sale                                                 1,530        1,530
     Deferred income taxes                                                5,818        5,818
                                                                      ---------    ---------
               Total current assets                                      39,284       35,081

Property and equipment                                                  140,631      131,953
     Less accumulated depreciation                                      (43,968)     (33,741)
                                                                      ---------    ---------
                                                                         96,663       98,212
Other assets                                                                 22           69
                                                                      ---------    ---------
                                                                      $ 135,969    $ 133,362
                                                                      =========    =========

                      LIABILITIES AND STOCKHOLDERS' EQUITY
Current liabilities:
     Accounts payable and accrued expenses                            $  12,324    $  11,745
     Accrued claims expense                                              13,239       15,041
     Current maturities of long-term debt                                     0        2,857
                                                                      ---------    ---------
          Total current liabilities                                      25,563       29,643

  Long-term debt, less current maturities                                45,000       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 - 4,096,834 in 1999 and 4,224,488 in 1998                   4,559        4,559
     Additional paid-in capital                                          32,833       32,858
     Retained earnings                                                   17,747       18,569
                                                                      ---------    ---------
                                                                         55,139       55,986
     Less common stock in treasury, 461,920 shares
       in 1999 and 334,266 shares in 1998, at cost                       (4,213)      (3,318)
                                                                      ---------    ---------
          Total stockholders' equity                                     50,926       52,668
                                                                      ---------    ---------
                                                                      $ 135,969    $ 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    Thirty-Nine Weeks Ended
                                                             October 1,   October 2,   October 1,   October 2,
                                                                1999         1998        1999          1998
                                                             ---------    ---------    ---------    ---------
                                                                 (In Thousands, Except Per Share Amounts)
<S>                                                          <C>          <C>          <C>          <C>
OPERATING REVENUE                                            $  58,893    $  55,102    $ 175,453    $ 174,405

OPERATING EXPENSES:

  Salaries, wages and fringe benefits                           21,650       17,119       62,007       54,956
  Operating supplies and expenses                               15,418       13,977       43,534       42,822
  Insurance, claims, taxes and licenses                          2,248        3,550        8,189       10,738
  Depreciation and amortization                                  4,632        4,595       13,573       13,769
  Purchased transportation and equipment rent                   12,739       12,588       38,945       38,755
  Other                                                          2,718        2,809        8,263        8,523
  Gain on sale of revenue equipment                                (93)        (798)        (601)      (1,005)
                                                             ---------    ---------    ---------    ---------
    TOTAL OPERATING EXPENSES                                    59,312       53,840      173,910      168,558
                                                             ---------    ---------    ---------    ---------
    OPERATING INCOME (LOSS)                                       (419)       1,262        1,543        5,847

Interest and other income                                          (15)          (8)         (36)        (934)
Interest expense                                                   793          874        2,504        2,700
                                                             ---------    ---------    ---------    ---------
                                                                   778          866        2,468        1,766
                                                             ---------    ---------    ---------    ---------

EARNINGS (LOSS) BEFORE INCOME TAXES AND EXTRAORDINARY ITEM      (1,197)         396         (925)       4,081
Income taxes                                                      (450)         165         (350)       1,640
                                                             ---------    ---------    ---------    ---------
NET EARNINGS (LOSS) BEFORE EXTRAORDINARY ITEM                     (747)         231         (575)       2,441

Expenses associated with the early extinguishment of
  debt, net of taxes                                                 0            0          247            0
                                                             ---------    ---------    ---------    ---------
NET EARNINGS (LOSS)                                          $    (747)   $     231    $    (822)   $   2,441
                                                             =========    =========    =========    =========

BASIC AND DILUTED EARNINGS (LOSS) PER COMMON SHARE:
    From operations                                          $   (0.18)   $    0.05    $   (0.14)   $    0.56
    From expenses associated with the early
      extinguishment of debt                                         0            0        (0.06)           0
                                                             ---------    ---------    ---------    ---------
    Net earnings (loss) per common share                     $   (0.18)   $    0.05    $   (0.20)   $    0.56
                                                             =========    =========    =========    =========
</TABLE>

See accompanying notes.





                                       2
<PAGE>   5

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

<TABLE>
<CAPTION>
                                                           Thirty-nine Weeks Ended
                                                            October 1,   October 2,
                                                               1999        1998
                                                             --------    --------
                                                                (In Thousands)
<S>                                                          <C>         <C>
NET CASH PROVIDED BY OPERATING
     ACTIVITIES                                              $  6,957    $ 16,232

CASH FLOWS FROM INVESTING ACTIVITIES:
   Purchases of property and equipment                        (22,798)    (19,527)
   Proceeds from disposition of property, equipment and
     assets held for sale                                      10,907      12,550
                                                             --------    --------
NET CASH FLOWS USED IN INVESTING ACTIVITIES                   (11,891)     (6,977)

CASH FLOWS FROM FINANCING ACTIVITIES:
   Purchases of common stock for treasury                        (960)       (468)
   Net increase in borrowings under
     revolving line of credit                                  17,000       1,000
   Repayment of long-term debt and capital leases             (11,428)     (8,296)
                                                             --------    --------
NET CASH FLOWS PROVIDED BY (USED IN)
     FINANCING ACTIVITIES                                       4,612      (7,764)
                                                             --------    --------
     Net Increase (Decrease) in Cash and Cash Equivalents        (322)      1,491

     Cash and Cash Equivalents at Beginning of Period             756         670
                                                             --------    --------
     Cash and Cash Equivalents at End of Period              $    434    $  2,161
                                                             ========    ========
NONCASH FINANCING ACTIVITIES
   Common stock issued for services                          $     40    $     36
                                                             ========    ========
</TABLE>

See accompanying notes.




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<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 third quarter of 1999 ended on Friday, October 1,
1999.

NOTE C- CREDIT FACILITIES AND DEBT

         During the quarter ended October 1, 1999, the Company's unsecured
revolving line of credit was amended to increase the line to $60,000,000 and
extend the maturity date to April 2001.

NOTE D- 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
the Company's 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 third quarter of 1999 increased 7% from the
comparable period of 1998 while the number of trucks in operation remained
consistent. The increase in operating revenue in the third quarter consisted of
a 3% increase from the Company's traditional over-the-road
temperature-controlled freight services and a 4% increase from the dry-van
over-the-road truckload division. An increase in the utilization of equipment
(10%) over the same quarter in 1998, was the primary factor contributing to the
increase in revenue. Revenue per total mile decreased 1% compared to the third
quarter of 1998. Fuel surcharges added slightly to revenues ($85,000) in the
third quarter of 1999. The Company had no fuel surcharges in 1998.

         Operating revenue during the first nine months of 1999 increased 1%
compared to the same period in 1998. The increase in 1999 reflects improvement
in equipment utilization during the third quarter offset by the negative impact
of the winter weather, during the first quarter, on 1999 revenue.

         The operating ratio increased from 97.7% to 100.7% for the third
quarter of 1999 compared to the same period in 1998. During the first nine
months of 1999, the operating ratio increased from 96.7% to 99.1%.

     During September 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. The
result of these increases was a rise in salary, wages and fringe benefits of 26%
for the third quarter and 13% for the first nine months of the year compared to
1998. Decreases in accidents, and their related costs, are partially the result
of the restructured pay package and its positive effect on the experience level
of drivers. Insurance, claims, taxes and licenses were $1,302,000 and $2,549,000
less for the third quarter and the first nine months, respectively, than the
same periods in 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. Although operating supplies and expenses increased for the
quarter and for the first nine months when compared to the prior year, various
components within the category decreased including equipment repair and wreck
expense. These decreases were offset by increases in the cost of fuel which had
the effect of increasing fuel expense, net of surcharges, by $1,200,000 for the
third quarter compared to the same period last year.

         As a result of the foregoing, operating income decreased by $1,681,000
and $4,304,000 for the third quarter and first nine months of 1999,
respectively, when compared to the comparable periods of 1998. For the first
nine months of 1999, interest and other income was $898,000 less than last year
principally as a result of the sale of the corporate office building during the
first quarter of 1998.

         Net earnings (loss) before extraordinary item decreased $978,000 and
$3,016,000 for the third quarter and the first nine months of 1999,
respectively, compared to the same periods in 1998. Basic and diluted earnings
per share before the extraordinary item, decreased $.24 to a loss of $.18 in the
third quarter of 1999 and decreased $.70 to a loss of $.14 for the first nine
months 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 thirty-nine weeks
ended October 1, 1999, the Company generated $6,957,000 in net cash from
operating activities.

         During the first nine months of 1999, net cash flows used in investing
activities by the Company were approximately $12 million. Net capital
expenditures for the remainder of 1999, primarily for revenue equipment, are
expected to be approximately $7 million. The Company entered into operating
leases for 400 trailers and for 65 tractors during the first nine months of
1999.




                                       5
<PAGE>   8

         The Company has a $60,000,000 unsecured revolving line of credit (the
"Revolver") with a syndication of banks. Borrowings under the Revolver of
$45,000,000 were outstanding at October 1, 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 1/4% to 1/2% per annum are charged on the unused
portion of this line. At October 1, 1999, borrowings under the Revolver was the
Company's only long-term debt outstanding.

         During the second 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 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 $5 million unsecured working
capital line of credit with a bank, all of which was available at October 1,
1999. Interest is at a rate based upon the Eurodollar rates with facility fees
at 3/8% 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 purchased
for $960,000 of which 50,000 shares for $356,000 were purchased 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. While all scheduled
changes and modifications have been completed, the Company is testing all
applications to ensure a seamless transition to the year 2000.

         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 time since that study, the conversion effort and timeline have been updated
to reflect progress on the overall project. Consistent with the original Year
2000 conversion timeline, all scheduled changes and modifications have been
completed. Currently testing of all applications includes performing detail
testing and actually changing the date to the year 2000 in certain systems. The
total project has cost 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.

         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 issue on their



                                       6
<PAGE>   9

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.

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 October 1, 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 October 29, 1999              /s/  Jack Liles
                                   ---------------------------------------------
                                   Jack Liles
                                   Chairman of the Board, President and Chief
                                   Executive Officer



Date October 29, 1999              /s/ Steven L. Dutro
                                   ---------------------------------------------
                                   Steven L. Dutro
                                   Senior Vice President and Chief Financial
                                   Officer





                                       9