<PAGE>   1



===============================================================================



                       SECURITIES AND EXCHANGE COMMISSION
                             WASHINGTON, D.C. 20549

                             ----------------------

                                    FORM 10-Q
(MARK ONE)
      [X]       QUARTERLY REPORT PURSUANT TO SECTION 13 OR 15(d)
                     OF THE SECURITIES EXCHANGE ACT OF 1934

                     FOR THE QUARTERLY PERIOD ENDED SEPTEMBER 30, 1998

                                       OR

      [_]      TRANSITION REPORT PURSUANT TO SECTION 13 OR 15(d)
                     OF THE SECURITIES EXCHANGE ACT OF 1934

                FOR THE TRANSITION PERIOD ENDED FROM __________ TO __________

                         COMMISSION FILE NUMBER 1-12380

                         ------------------------------

                                  AVIALL, INC.
             (Exact name of Registrant as specified in its Charter)

              DELAWARE                                    65-0433083
  (State or other jurisdiction of                     (I.R.S. Employer
   incorporation or organization)                     Identification No.)

       2075 DIPLOMAT DRIVE
           DALLAS, TEXAS                                   75234-8999
(Address of principal executive offices)                   (Zip Code)

                                 (972) 406-2000
              (Registrant's telephone number, including area code)


     Indicate by check [X] 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 (or for such shorter period that the
Registrant was required to file such reports), and (2) has been subject to such
filing requirements for the past 90 days.  Yes    [X]      No    [ ]

     The number of shares of Common Stock, par value $.01 per share, outstanding
at November 5, 1998 was 18,171,483.



===============================================================================


<PAGE>   2





                         PART I - FINANCIAL INFORMATION



ITEM 1:  FINANCIAL STATEMENTS

                                  AVIALL, INC.
                        CONSOLIDATED STATEMENTS OF INCOME
                    (DOLLARS IN THOUSANDS, EXCEPT SHARE DATA)
                                   (UNAUDITED)

<TABLE>
<CAPTION>

                                                              Three months ended                    Nine months ended
                                                                 September 30,                         September 30,
                                                        ------------------------------        ------------------------------
                                                            1998               1997               1998               1997
                                                        -----------        -----------        -----------        -----------

<S>                                                     <C>                    <C>                <C>                <C>    
Net sales                                               $   102,126            100,267            305,105            288,012
Cost of sales                                                76,672             75,339            228,632            215,807
                                                        -----------        -----------        -----------        -----------
Gross profit                                                 25,454             24,928             76,473             72,205
Operating and other expenses:
   Selling and administrative expenses                       17,132             17,017             51,800             50,035
   Nonrecurring item                                           --                 --                 --               (1,436)
   Interest expense                                             809                752              1,892              2,477
                                                        -----------        -----------        -----------        -----------
Earnings from continuing operations before income taxes       7,513              7,159             22,781             21,129
Provision for income taxes                                      232                123                693              1,023
                                                        -----------        -----------        -----------        -----------
Earnings from continuing operations                           7,281              7,036             22,088             20,106
Discontinued operations:
   Gain on disposal                                            --                 --                2,083               --
                                                        -----------        -----------        -----------        -----------
Earnings from discontinued operations                          --                 --                2,083               --
                                                        -----------        -----------        -----------        -----------
Net earnings                                            $     7,281              7,036             24,171             20,106
                                                        ===========        ===========        ===========        ===========

Basic net earnings per share:
   Earnings from continuing operations                  $      0.39               0.36               1.13               1.02
   Earnings from discontinued operations                       --                 --                 0.11               --
                                                        -----------        -----------        -----------        -----------
Net earnings                                            $      0.39               0.36               1.24               1.02
                                                        ===========        ===========        ===========        ===========
Weighted average common shares                           18,742,140         19,742,977         19,474,933         19,650,240
                                                        ===========        ===========        ===========        ===========
Diluted net earnings per share:
   Earnings from continuing operations                  $      0.38               0.35               1.11               1.01
   Earnings from discontinued operations                       --                 --                 0.11               --
                                                        -----------        -----------        -----------        -----------
Net earnings                                            $      0.38               0.35               1.22               1.01
                                                        ===========        ===========        ===========        ===========
Weighted average common and potentially dilutive
   common shares                                         19,038,745         20,249,746         19,844,491         19,974,013
                                                        ===========        ===========        ===========        ===========

</TABLE>



See accompanying notes to consolidated financial statements.

                                       2

<PAGE>   3





                                  AVIALL, INC.
                           CONSOLIDATED BALANCE SHEETS
                    (DOLLARS IN THOUSANDS, EXCEPT SHARE DATA)

<TABLE>
<CAPTION>

                                                                                              September 30,    December 31,
                                                                                                  1998            1997
                                                                                              -------------    ------------
                                                                                               (Unaudited)

<S>                                                                                             <C>                <C>  
ASSETS
Current assets:
   Cash                                                                                         $  2,420           7,556
   Receivables                                                                                    61,345          59,119
   Inventories                                                                                    88,416          73,414
   Prepaid expenses and other current assets                                                       1,582           1,627
   Deferred income taxes                                                                          11,795          11,795
                                                                                                --------        --------
Total current assets                                                                             165,558         153,511
                                                                                                --------        --------

Property, plant and equipment                                                                      9,988           9,758
Intangible assets                                                                                 53,513          55,134
Deferred income taxes                                                                             37,479          37,530
Other assets                                                                                       3,389           3,459
                                                                                                --------        --------
Total assets                                                                                    $269,927         259,392
                                                                                                ========         =======

LIABILITIES AND SHAREHOLDERS' EQUITY 
Current liabilities:
   Current portion of long-term debt                                                            $ 13,270           8,556
   Accounts payable                                                                               29,317          27,765
   Accrued expenses                                                                               35,020          40,309
                                                                                                --------        --------
Total current liabilities                                                                         77,607          76,630
                                                                                                --------        --------

Long-term debt                                                                                    40,000          28,004
Other liabilities                                                                                 25,104          27,397
Shareholders' equity (includes common stock of $.01 par value per share with
   80,000,000 shares authorized; 20,171,483 shares and 19,900,195 shares issued
   at September 30, 1998 and at December 31, 1997, respectively; 18,171,483
   shares and 19,900,195 shares outstanding at September 30, 1998 and at 
   December 31, 1997, respectively; preferred stock of $.01 par value per share
   with 10,000,000 shares authorized and no shares issued and outstanding)                       127,216         127,361
                                                                                                --------        --------
Total liabilities and shareholders' equity                                                      $269,927         259,392
                                                                                                ========         =======
</TABLE>




See accompanying notes to consolidated financial statements.


                                       3
<PAGE>   4




                                  AVIALL, INC.
                      CONSOLIDATED STATEMENTS OF CASH FLOWS
                             (DOLLARS IN THOUSANDS)
                                   (UNAUDITED)

<TABLE>
<CAPTION>

                                                                            Nine months ended
                                                                              September 30,
                                                                       --------------------------
                                                                          1998             1997
                                                                       --------------------------
<S>                                                                    <C>                <C>   
CASH FLOWS FROM OPERATING ACTIVITIES:
   Net earnings                                                        $ 24,171           20,106
   Gain on disposal of discontinued operations                           (2,083)            --
   Nonrecurring item                                                       --             (1,436)
   Depreciation and amortization                                          4,307            4,069
   Compensation expense on restricted stock awards                          173             --
   Deferred income taxes                                                     19               18
   Changes in:
     Receivables                                                         (1,648)          (5,854)
     Inventories                                                        (14,958)            (861)
     Accounts payable                                                     1,552           (2,577)
     Accrued expenses                                                    (3,828)          (7,527)
     Other, net                                                          (2,535)          (1,852)
                                                                       --------         --------
                                                                          5,170            4,086
                                                                       --------         --------
CASH FLOWS FROM INVESTING ACTIVITIES:
   Proceeds received from repayment of note receivable                     --             12,000
   Capital expenditures                                                  (2,621)          (2,127)
   Sales of property, plant and equipment                                    95              105
                                                                       --------         --------
                                                                         (2,526)           9,978
                                                                       --------         --------
CASH FLOWS FROM FINANCING ACTIVITIES:
   Debt repaid                                                           (6,552)         (13,772)
   Net change in revolving credit facility                               23,262           (2,189)
   Issuance of common stock                                               3,243            3,227
   Purchase of treasury stock                                           (27,733)            --
                                                                       --------         --------
                                                                         (7,780)         (12,734)
                                                                       --------         --------
Change in cash                                                           (5,136)           1,330
Cash, beginning of period                                                 7,556            4,191
                                                                       --------         --------
Cash, end of period                                                    $  2,420            5,521
                                                                       ========         ========
CASH PAID FOR INTEREST AND INCOME TAXES:
   Interest                                                            $  1,900            3,030
   Income taxes                                                        $  1,085            1,098

</TABLE>



See accompanying notes to consolidated financial statements.


                                        4

<PAGE>   5



                                  AVIALL, INC.
                   NOTES TO CONSOLIDATED FINANCIAL STATEMENTS



NOTE 1 - BASIS OF PRESENTATION

     The accompanying unaudited financial statements have been prepared in
accordance with generally accepted accounting principles for interim financial
information and with the instructions to Form 10-Q and Article 10 of Regulation
S-X. Accordingly, these financial statements 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 only of normal recurring adjustments) considered necessary for a
fair presentation have been included. Operating results for the three- and
nine-month periods ended September 30, 1998 are not necessarily indicative of
the results that may be expected for the year ending December 31, 1998. For
further information, refer to the financial statements and footnotes thereto
included in Aviall, Inc.'s Form 10-K for the year ended December 31, 1997.

NOTE 2 - GAIN ON DISCONTINUED OPERATIONS

     A gain from discontinued operations recorded in the second quarter of 1998
resulted from a change in estimate for retained obligations.



                                       5

<PAGE>   6



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

OVERVIEW. The following discussion and analysis should be read in conjunction
with the information set forth under Item 7: Management's Discussion and
Analysis of Financial Condition and Results of Operations on pages 13 through 19
of Aviall, Inc.'s (the "Company") Form 10-K for the year ended December 31,
1997.

RESULTS OF OPERATIONS - THREE MONTHS ENDED SEPTEMBER 30, 1998 COMPARED TO THREE
MONTHS ENDED SEPTEMBER 30, 1997. Net sales for the third quarter of 1998 were
$102.1 million, up $1.9 million, or 1.9%, from the $100.3 million recorded in
the same 1997 quarter. Parts distribution sales grew $1.3 million, or 1.4%,
compared to the same period prior year. Sales growth continued to be strong in
the general aviation segment but was offset by lower sales in Asia and the
airline market segment. Inventory information services revenues increased 8.5%
compared to the prior year.

     Gross profit of $25.5 million was $0.5 million higher than the $24.9
million in the 1997 third quarter. Gross profit as a percentage of sales was
unchanged at 24.9%.

     Selling and administrative expenses increased $0.1 million, or 0.7%, to
$17.1 million in the third quarter of 1998. The increase primarily resulted from
increased compensation expense.

     Interest expense was slightly higher than in the third quarter of 1997,
reflecting higher debt levels partially offset by lower interest rates.

RESULTS OF OPERATIONS - NINE MONTHS ENDED SEPTEMBER 30, 1998 COMPARED TO NINE
MONTHS ENDED SEPTEMBER 30, 1997. Net sales for the first three quarters of 1998
were $305.1 million, up $17.1 million, or 5.9%, from the $288.0 million recorded
in the same period of 1997. Parts distribution sales increased $15.6 million, or
5.8%, with higher sales in all geographic regions. The growth rate for sales has
declined in the domestic, Latin America and particularly Asian regions. Strong
general aviation sales growth helped offset the lower airline segment sales
growth.

     Gross profit of $76.5 million in the first nine months of 1998 increased
$4.3 million, or 5.9%, from the $72.2 million in the same period of 1997. Gross
profit as a percentage of sales remained unchanged at 25.1%.

     Selling and administrative expenses increased $1.8 million, or 3.5%, to
$51.8 million in the first three quarters of 1998. The increase primarily
resulted from increased salary, benefits and sales commissions.

     Interest expense was lower than in the first nine months of 1997,
reflecting lower average debt balances and lower interest rates. Tax expense
decreased due to a revised estimated tax rate of 3% for the year, resulting from
lower profit projections for the Company's foreign subsidiaries.

     The 1997 results include a $1.4 million nonrecurring gain from the full
repayment in January 1997 of a discounted note received in connection with the
1995 sale of the business aviation engine overhaul, and aircraft and terminal
services operations. The 1998 gain from discontinued operations resulted from a
revised estimate for retained liabilities, primarily product liability
insurance.

FINANCIAL CONDITION. Cash flows from operations were $5.2 million for the first
three quarters of 1998 and $4.1 million in the comparable 1997 period. The
improved cash flow was primarily due to higher net earnings, offset by increased
inventory purchases for higher anticipated sales volume.

     Capital expenditures in the first nine months of 1998 were primarily
related to implementation of the new financial and operating system software and
related computer hardware.

     In January 1998, the Company announced a $30 million share repurchase
program to buyback up to 10% of the Company's outstanding common stock over a
two year period in open market transactions, depending on market, economic and
other factors. The Company completed this program during the third quarter. Two
million shares were purchased at a total cost of $27.7 million. The Company
primarily used debt to finance this purchase.

     In January 1997, a $12.0 million unsecured subordinated note received in
connection with the 1995 sale of the business aviation engine repair operation
was repaid. The Company applied the proceeds as a permanent reduction of the
term loan under the 1996 bank agreement. Because of the uncertainty regarding
the collection of the note when it was received in March 1995, the Company
carried the note at a discounted value of $10.5 million.



                                       6



<PAGE>   7


     The Company's income tax expense continues to be substantially lower than
the U.S. federal statutory rate due to the utilization of the large U.S. net
operating loss ("NOL") and the corresponding decrease in the valuation allowance
on the deferred tax assets. The Company's tax expense is primarily related to
foreign taxes on foreign operations. For U.S. federal tax purposes as of
December 31, 1997, the Company had an estimated NOL carryforward of
approximately $200 million, substantially expiring in 2009-2011, which is
expected to minimize U.S. federal income tax cash payments for several years. If
certain substantial changes in the Company's ownership should occur, there would
be an annual limitation on the amount of the NOL carryforward that could be
utilized.

     The Company believes that its expected cash flow from operations and
availability under its revolving lines of credit are sufficient to meet its
current working capital and operating needs.

YEAR 2000 COMPUTER SYSTEM COMPLIANCE. Many existing computer software and
hardware programs refer to the year by only using the last two digits of the
year. These computer programs will not properly interpret the year 2000. These
programs, unless upgraded, could fail or create erroneous results causing a
disruption in the operations of a company.

     STATE OF READINESS. During 1998, hardware and system software reviews for
Year 2000 compliance, including information technology ("IT") and non-IT
systems, were conducted by the Company with the assistance of outside
consultants. In addition, the Company is assessing its exposure from external
sources to Year 2000 failures, including major suppliers, customers and
third-party providers. The Company is replacing its financial and parts
distribution applications software with Year 2000 compliant systems. The
replacement of the financial software was implemented on schedule in the second
quarter of 1998. The parts distribution applications software replacement is
scheduled for implementation in the first quarter of 1999. Inventory information
services functions on internally developed applications software. The program
modifications to make this proprietary software Year 2000 compliant have been
completed. Testing and validation of these modifications will be conducted
during the fourth quarter of 1998 and the first quarter of 1999. The following
is a table showing the Company's state of Year 2000 readiness based on
management's assessment:

                               STATE OF READINESS
                            AS OF SEPTEMBER 30, 1998

                  INTERNAL IT AND NON-IT SYSTEMS AND EQUIPMENT
<TABLE>
<CAPTION>

                                                             ESTIMATED
                                                              PERCENT          ESTIMATED
        PHASE                                                COMPLETE       COMPLETION DATE
        -----                                                ---------      ---------------

<S>                                                          <C>            <C> 
Awareness                                                       100%       Complete
Assessment changes required                                      95%       1st Quarter 1999
Remediation or replacement                                       75%       2nd Quarter 1999
Testing                                                          20%       3rd Quarter 1999
Contingency planning                                              5%       2nd Quarter 1999

</TABLE>

                        SUPPLIERS, CUSTOMERS AND THIRD-PARTY PROVIDERS
<TABLE>
<CAPTION>
                                                             ESTIMATED
                                                              PERCENT          ESTIMATED
        PHASE                                                COMPLETE       COMPLETION DATE
        -----                                                ---------      ---------------
<S>                                                          <C>           <C>      
Awareness - Identify companies                                  100%       Complete
Assessment Questionnaire completed by major suppliers            20%       1st Quarter 1999
Detail assessment review with 3rd party providers
   (i.e. MCI, IBM, Lawson, UPS)                                  10%       1st Quarter 1999
Review contractual commitments                                    0%       1st Quarter 1999
Risk Assessment                                                  10%       2nd Quarter 1999
Contingency planning                                              5%       2nd Quarter 1999
Testing as applicable                                             0%       3rd Quarter 1999

</TABLE>



                                      7


<PAGE>   8



     COSTS. The Company is replacing its parts distribution applications and
financial software with an integrated enterprise system at a cost of
approximately $5 million which is being capitalized. The replacement resulted
from both the need to enhance the efficiencies and effectiveness of the
distribution operating system by replacing several old legacy systems and to
address the Year 2000 issue. Approximately $200,000 has been expensed to date
related to parts distribution for Year 2000. An estimated additional $300,000
will be expensed. The cost expensed to date to modify the inventory information
services operating software was $125,000. An additional $150,000 will be
required to complete the project, including testing.

     RISKS/CONTINGENCY PLANS: In management's assessment, the most likely
worst case scenario for Year 2000 non-compliance for parts distribution would
result if suppliers were unable to ship inventory to meet market demands. In
addition, parts distribution does limited electronic data interchange ("EDI")
with both suppliers and customers. EDI suppliers or customers could be processed
manually if EDI failed from either side. Management's assessment for inventory
information services most likely worst case scenario would result if either the
listing companies were unable to update their data or clients were unable to
access the Company's database due to their own systems being non-Year 2000
compliant. The Company depends on third-party providers for key services such as
telecommunications, utilities and transportation. Interruption of these services
could, in management's view, have a material impact on the operations of the
Company. The Company has begun to evaluate the readiness of these critical
suppliers. The Company is in the early phase of developing Year 2000 contingency
plans and determining the extent of such plans. Although Aviall's management
presently believes the Company is taking appropriate steps to assess and correct
its Year 2000 issues, due to the general uncertainty inherent in the Year 2000
issue and the readiness of third parties, Aviall is unable to determine whether
Year 2000 will have a material adverse effect on the Company's results of
operations or financial condition.

OUTLOOK. The Company's financial and parts distribution operating systems are
critical to Aviall's success. Implementation of complex new software systems
carries certain risks that may affect normal operations. Sales in the fourth
quarter of 1998 and the first quarter of 1999 may be negatively impacted due to
training and early system utilization. Training expenses in the fourth quarter
of 1998 are estimated up to $750,000. Management believes the Company's
implementation plan combined with appropriate training throughout the
organization will minimize these risks.

     Aviall primarily participates in the global aviation aftermarket through
its core aviation parts distribution and inventory information services
businesses. The Company can be affected by the general economic cycle,
particularly as it influences flight activity in commercial, business and
general aviation. Economic conditions in the past several years have led to an
improved aviation market, and provided the Company with the opportunity for
growth.

     The Company serves a significant number of customers in the Asian and Latin
America markets. Recent events, particularly in Asia, have resulted in decreased
economic activity and increased currency fluctuations relative to the U.S.
dollar. These factors have depressed air travel which impacts the Company's
customers' need for aircraft parts and potentially their ability to pay in a
timely manner. In the third quarter of 1998, business in Asia fell below the
levels achieved in 1997. The outlook for the rest of 1998 for this region
appears to be weak. The Company continues to closely monitor these events.
Overall, the Company expects sales for the rest of the year to be similar to
that reported in the third quarter of 1998.



                                       8


<PAGE>   9



CERTAIN FORWARD-LOOKING STATEMENTS. This report contains certain forward-looking
statements (as such term is defined in the Private Securities Litigation Reform
Act of 1995) relating to the Company that are based on the beliefs of the
management of the Company, as well as assumptions and estimates made by and
information currently available to the Company's management. When used in this
report, the words "anticipate," "believe," "estimate," "expect," "intend" and
similar expressions, as they relate to the Company or the Company's management,
identify forward-looking statements. Such statements reflect the current views
of the Company with respect to future events and are subject to certain risks,
uncertainties and assumptions relating to the operations and results of
operations of the Company as well as its customers and suppliers, including as a
result of competitive factors and pricing pressures, shifts in market demand,
the effects of the Year 2000 issue on the Company and its suppliers and
customers, general economic conditions and other factors including among others,
those that effect flight activity in commercial, business and general aviation,
the business activities of the Company's customers and suppliers and
developments in information and communication technology. Should one or more of
these risks or uncertainties materialize, or should underlying assumptions or
estimates prove incorrect, actual results may vary materially from those
described herein as anticipated, believed, estimated, expected or intended.



                                        9


<PAGE>   10



                           PART II - OTHER INFORMATION


ITEM 6:  EXHIBITS AND REPORTS ON FORM 8-K

     (a)  Exhibits

          27.1     Financial Data Schedule

     (b)  Reports on Form 8-K

          No reports on Form 8-K have been filed during the quarter for which
this report is filed.



                                       10


<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.

                                         AVIALL, INC.

November 9, 1998                         By /s/ Jacqueline K. Collier
                                            ----------------------------------
                                            Jacqueline K. Collier
                                            Vice President and Controller
                                            Principal Accounting Officer


November 9, 1998                            /s/ Cornelius Van Den Handel
                                            ----------------------------------
                                            Cornelius Van Den Handel
                                            Vice President and Treasurer
                                            Principal Financial Officer





                                       11

<PAGE>   12



                                INDEX TO EXHIBITS


    Exhibit
    Number        Description
------------------------------------------------------------------------------

    27.1          Financial Data Schedule