<PAGE>   1
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                       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 JUNE 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 August 5, 1998 was 19,057,992.

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

<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            Six months ended
                                                                        June 30,                    June 30,
                                                            ---------------------------      --------------------------
                                                                1998            1997            1998             1997
                                                            -----------      ----------      ----------      ----------
<S>                                                         <C>                  <C>            <C>             <C>    
Net sales                                                   $   104,949          96,063         202,979         187,745
Cost of sales                                                    78,970          71,830         151,960         140,468
                                                            -----------      ----------      ----------      ----------
Gross profit                                                     25,979          24,233          51,019          47,277
Operating and other expenses:
   Selling and administrative expenses                           17,481          16,827          34,668          33,018
   Nonrecurring item                                               --              --              --            (1,436)
   Interest expense                                                 576             991           1,083           1,725
                                                            -----------      ----------      ----------      ----------
Earnings from continuing operations before income taxes           7,922           6,415          15,268          13,970
Provision for income taxes                                           94             288             461             900
                                                            -----------      ----------      ----------      ----------
Earnings from continuing operations                               7,828           6,127          14,807          13,070
Discontinued operations:
   Gain on disposal                                               2,083            --             2,083            --
                                                            -----------      ----------      ----------      ----------
Earnings from discontinued operations                             2,083            --             2,083            --
                                                            -----------      ----------      ----------      ----------
Net earnings                                                $     9,911           6,127          16,890          13,070
                                                            ===========      ==========      ==========      ==========

Basic net earnings per share:
   Earnings from continuing operations                      $      0.40            0.31            0.75            0.67
   Earnings from discontinued operations                           0.10            --              0.10            --
                                                            -----------      ----------      ----------      ----------
Net earnings                                                $      0.50            0.31            0.85            0.67
                                                            ===========      ==========      ==========      ==========
Weighted average common shares                               19,727,636      19,629,361      19,847,404      19,603,104
                                                            ===========      ==========      ==========      ==========
Diluted net earnings per share:
   Earnings from continuing operations                      $      0.39            0.31            0.73            0.66
   Earnings from discontinued operations                           0.10            --              0.10            --
                                                            -----------      ----------      ----------      ----------
Net earnings                                                $      0.49            0.31            0.83            0.66
                                                            ===========      ==========      ==========      ==========
Weighted average common and potentially dilutive
   common shares                                             20,119,859      19,955,833      20,253,439      19,835,382
                                                            ===========      ==========      ==========      ==========
</TABLE>


See accompanying notes to consolidated financial statements.

                                       2
<PAGE>   3




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

<TABLE>
<CAPTION>

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

ASSETS
Current assets:
<S>                                                                                  <C>             <C>  
   Cash                                                                              $  2,089        7,556
   Receivables                                                                         64,095       59,119
   Inventories                                                                         80,848       73,414
   Prepaid expenses and other current assets                                            1,548        1,627
   Deferred income taxes                                                               11,795       11,795
                                                                                     --------      -------
Total current assets                                                                  160,375      153,511
                                                                                     --------      -------

Property, plant and equipment                                                          10,328        9,758
Intangible assets                                                                      54,027       55,134
Deferred income taxes                                                                  37,506       37,530
Other assets                                                                            3,463        3,459
                                                                                     --------      -------
Total assets                                                                         $265,699      259,392
                                                                                     ========      =======



LIABILITIES AND SHAREHOLDERS' EQUITY 
Current liabilities:
   Current portion of long-term debt                                                 $ 11,320        8,556
   Accounts payable                                                                    37,067       27,765
   Accrued expenses                                                                    34,321       40,309
                                                                                     --------      -------
Total current liabilities                                                              82,708       76,630
                                                                                     --------      -------

Long-term debt                                                                         24,000       28,004
Other liabilities                                                                      26,369       27,397
Shareholders' equity (includes common stock of $.01 par value per share with
   80,000,000 shares authorized; 20,153,492 shares and 19,900,195 shares issued
   at June 30, 1998 and at December 31, 1997, respectively; 19,125,592 shares
   and 19,900,195 shares outstanding at June 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)                            132,622      127,361
                                                                                     --------      -------
Total liabilities and shareholders' equity                                           $265,699      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>

                                                          Six months ended June 30,
                                                          -------------------------
                                                              1998           1997
                                                           --------        ------
<S>                                                        <C>             <C>   
CASH FLOWS FROM OPERATING ACTIVITIES:
   Net earnings                                            $ 16,890        13,070
   Gain on disposal of discontinued operations               (2,083)         --
   Nonrecurring item                                           --          (1,436)
   Depreciation and amortization                              2,808         2,735
   Compensation expense on restricted stock awards              115          --
   Deferred income taxes                                          8            12
   Changes in:
     Receivables                                             (4,398)       (5,085)
     Inventories                                             (7,390)       (2,024)
     Accounts payable                                         9,302         2,697
     Accrued expenses                                        (4,527)       (7,456)
     Other, net                                              (1,021)         (233)
                                                           --------        ------
                                                              9,704         2,280
                                                           --------        ------
CASH FLOWS FROM INVESTING ACTIVITIES:
   Proceeds received from repayment of note receivable         --          12,000
   Capital expenditures                                      (2,104)       (1,094)
   Sales of property, plant and equipment                       (83)           96
                                                           --------        ------
                                                             (2,187)       11,002
                                                           --------        ------
CASH FLOWS FROM FINANCING ACTIVITIES:
   Debt repaid                                               (4,549)      (12,510)
   Net change in revolving credit facility                    3,309        (2,069)
   Issuance of common stock                                   3,078         1,105
   Purchase of treasury stock                               (14,822)         --
                                                           --------        ------
                                                            (12,984)      (13,474)
                                                           --------        ------
Change in cash                                               (5,467)         (192)
Cash, beginning of period                                     7,556         4,191
                                                           --------        ------
Cash, end of period                                        $  2,089         3,999
                                                           ========        ======

CASH PAID FOR INTEREST AND INCOME TAXES:
   Interest                                                $  1,138         2,274
   Income taxes                                            $    633           991
</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
six-month periods ended June 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 JUNE 30, 1998 COMPARED TO THREE
MONTHS ENDED JUNE 30, 1997. Net sales for the second quarter of 1998 were $104.9
million, up $8.9 million, or 9.3%, from the $96.1 million recorded in the same
1997 quarter. Sales growth was strong in the United States, with the largest
percentage gains in the Latin America, Australia and European markets. A large
government contract sale in Asia offset a decrease in that market's base
business.

     Gross profit of $26.0 million was $1.7 million higher than the $24.2
million in the 1997 second quarter. Gross profit as a percentage of sales
decreased from 25.2% to 24.8%. This decrease in gross profit percentage was
primarily a result of the lower margin on the government contract sale in Asia.

     Selling and administrative expenses increased $0.7 million, or 3.9%, to
$17.5 million in the second quarter of 1998. The increase primarily resulted
from increased salary, benefits and sales commissions.

     Interest expense was lower than in the second quarter of 1997, reflecting
lower borrowings and lower interest rates. Tax expense decreased due to a
revised estimated tax rate of 3% for the year, resulting from lower full year
profit projections for the foreign entities.

     A gain in discontinued operations resulted from revised estimates for
retained liabilities, primarily product liability insurance.

RESULTS OF OPERATIONS - SIX MONTHS ENDED JUNE 30, 1998 COMPARED TO SIX MONTHS
ENDED JUNE 30, 1997. Net sales for the first half of 1998 were $203.0 million,
up $15.2 million, or 8.1%, from the $187.7 million recorded in the same half of
1997. Sales continued to grow in all major business segments and geographic
regions, although a large government contract in Asia offset a decrease in the
region's base business.

     Gross profit of $51.0 million in the first six months increased $3.7
million, or 7.9%, from the $47.3 million in the first half of 1997. Gross profit
as a percentage of sales decreased slightly from 25.2% to 25.1%.

     Selling and administrative expenses increased $1.7 million, or 5.0%, to
$34.7 million in the first two quarters of 1998. The increase primarily resulted
from increased salary, benefits and sales commissions.

     Interest expense was lower than in the first half of 1997, reflecting lower
borrowings, lower interest rates and higher interest income from the larger
average cash balance.

     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 discontinued operations gain is discussed above.

FINANCIAL CONDITION. Cash flows from operations were $9.7 million in the first
six months of 1998 and $2.3 million in the comparable 1997 period. The improved
cash flow in 1998 was mostly due to the higher net earnings, higher accounts
payable primarily due to increased inventory purchases and lower payments
related to the retained liabilities for previously owned businesses.

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

     In January 1998, the Company's Board of Directors authorized a $30 million
share repurchase program to buyback up to 10% of the Company's outstanding
common stock over the next two years in open market transactions, depending on
market, economic and other factors. The Company presently intends to use
existing cash balances and future cash flows to fund this program; however, the
Company may also use borrowings under its existing credit facility to make
purchases. Through the second quarter of 1998, the Company has purchased an
aggregate of 1,027,900 shares for a total cost of $14.8 million under this
program. Management does not expect the share repurchase program to restrict the
Company from pursuing other opportunities for growth.

     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 and U.S. federal alternative minimum tax.
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. Improvements in earnings should
further enhance the Company's access to capital and enable the Company to
finance possible future investment opportunities.

OUTLOOK. As previously reported, the Company is replacing its financial and
parts distribution applications software. The replacement of the financial
systems software was implemented on schedule during second quarter. The parts
distribution software replacement is scheduled for implementation early in 1999.
Estimated training expenses in the fourth quarter 1998 are expected to be up to
$1 million.

     The Company's financial and parts distribution 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
first quarter of 1999 may be negatively impacted due to training and early
system utilization. Management believes their implementation process and
strategy combined with appropriate training throughout the organization will
minimize these risks.

     The new financial and parts distribution systems are Year 2000 compliant. A
year 2000 hardware and system software review was conducted by an outside
consultant during first half of 1998. Recommendations resulting from the review
will be implemented by year-end 1998. Based on the implementation and assessment
dates, management believes implementation will be completed in a timely manner
and there will be no material effect from Year 2000 on its future financial
results.

     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. Current favorable economic conditions 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 customers' need
for aircraft parts and potentially their ability to pay in a timely manner.
Without a large sale to a government customer in the second quarter of 1998,
sales in Asia would have fallen below the levels achieved in 1997. Management
expects business in Asia to remain soft for the balance of 1998. The Company
continues to closely monitor these events.

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,
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.

                                       7
<PAGE>   8



                           PART II - OTHER INFORMATION


ITEM 4:  SUBMISSION OF MATTERS TO A VOTE OF SECURITY HOLDERS

     The Company's Annual Meeting of Shareholders was held on May 22, 1998, at
which meeting the shareholders took action with respect to four proposals, (i)
the election of Robert G. Lambert and Donald R. Muzyka to serve as directors of
the Company for a term expiring at the Company's 2001 Annual Meeting of
Shareholders, (ii) the adoption of the Aviall, Inc. 1998 Stock Incentive Plan,
(iii) the approval of an amendment to the Aviall, Inc. Directors Stock Plan and
(iv) the ratification of the appointment of PricewaterhouseCoopers LLP to serve
as independent auditors for the Company and its subsidiaries for the fiscal year
ending December 31, 1998.
     The number of votes cast for, against or withheld, as well as the number of
abstentions as to each proposal is set forth below. There were no broker
non-votes with respect to any of the proposals.
<TABLE>
<CAPTION>

                                              Election of Directors
                                              ---------------------

                                                 Total Votes For              Total Votes Withheld
                                                 ---------------              --------------------
       <S>                                        <C>                               <C>   
          Robert G. Lambert                        17,650,266                        60,611

          Donald R. Muzyka                         17,652,665                        58,212
</TABLE>

     The other directors of the Company whose terms of office continued after
the meeting were Richard J. Schnieders, Bruce N. Whitman, Eric E. Anderson and
Henry A. McKinnell.
<TABLE>
<CAPTION>

                             Adoption of the Aviall, Inc. 1998 Stock Incentive Plan
                             ------------------------------------------------------

                 For                                 Against                         Abstain
                 ---                                 -------                         -------
            <S>                                    <C>                              <C>
             14,577,482                             2,492,935                        640,460

                        Approval of Amendment to the Aviall, Inc. Directors Stock Plan
                        --------------------------------------------------------------

                 For                                 Against                         Abstain
                 ---                                 -------                         -------
             15,008,913                             2,147,015                        554,949

                              Ratification of Selection of Independent Auditors
                              -------------------------------------------------

                 For                                 Against                         Abstain
                 ---                                 -------                         -------
             17,683,660                              14,551                          12,666
</TABLE>


ITEM 6:  EXHIBITS AND REPORTS ON FORM 8-K

     (a)  Exhibits

          10.1     Aviall, Inc. 1998 Directors Stock Plan

          10.2     Aviall, Inc. 1998 Stock Incentive Plan

          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.

                                       8

<PAGE>   9



                                   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.

August 7, 1998                              By   /s/ Jacqueline K. Collier
                                                 ------------------------------ 
                                                 Jacqueline K. Collier
                                                 Vice President and Controller
                                                 Principal Accounting Officer


August 7, 1998                                   /s/ Cornelius Van Den Handel
                                                 ------------------------------ 
                                                 Cornelius Van Den Handel
                                                 Vice President and Treasurer
                                                 Principal Financial Officer



                                       9

<PAGE>   10



                                INDEX TO EXHIBITS


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

    10.1          Aviall, Inc. 1998 Directors Stock Plan

    10.2          Aviall, Inc. 1998 Stock Incentive Plan

    27.1          Financial Data Schedule