<PAGE>   1
                                  UNITED STATES

                       SECURITIES AND EXCHANGE COMMISSION

                             Washington, D.C. 20549

                                    FORM 10-Q

[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 from         to

Commission File Number                1-7077


                           GTE SOUTHWEST INCORPORATED
             (EXACT NAME OF REGISTRANT AS SPECIFIED IN ITS CHARTER)

              DELAWARE                                  75-0573444
   (STATE OR OTHER JURISDICTION OF          (I.R.S. EMPLOYER IDENTIFICATION NO.)
   INCORPORATION OR ORGANIZATION)

         600 Hidden Ridge                                 75038
           Irving, Texas
(ADDRESS OF PRINCIPAL EXECUTIVE OFFICES)               (ZIP CODE)

Registrant's telephone number, including area code       972-718-5600


             (Former name, former address and former fiscal year, if
                           changed since last report)


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 (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 Company had 6,500,000 shares of $100 stated value common stock outstanding
at July 31, 1998. The Company's common stock is 100% owned by GTE Corporation.


<PAGE>   2
PART I.  FINANCIAL INFORMATION

GTE Southwest Incorporated
CONDENSED STATEMENTS OF INCOME

<TABLE>
<CAPTION>
                                             Three Months Ended            Six Months Ended
                                                   June 30,                   June 30,
                                            ---------------------     -----------------------
                                              1998         1997          1998          1997
                                            --------     --------     ---------      --------
                                                         (Thousands of Dollars)
<S>                                         <C>          <C>          <C>            <C>     
REVENUES AND SALES
   Local services                           $179,484     $154,633     $ 353,683      $313,364
   Network access services                   183,794      171,443       349,836       329,864
   Toll services                              22,001       35,533        46,773        76,157
   Other services and sales                   68,905       49,733       127,890       109,661
                                            --------     --------     ---------      --------

     Total revenues and sales                454,184      411,342       878,182       829,046
                                            --------     --------     ---------      --------

OPERATING COSTS AND EXPENSES
   Cost of services and sales                168,168      144,352       329,835       273,364
   Selling, general and administrative        77,016       64,550       144,567       115,001
   Depreciation and amortization              90,978       91,108       183,506       184,162
                                            --------     --------     ---------      --------

     Total operating costs and expenses      336,162      300,010       657,908       572,527
                                            --------     --------     ---------      --------

OPERATING INCOME                             118,022      111,332       220,274       256,519

OTHER EXPENSE
   Interest - net                             17,573       13,119        34,128        27,623
   Other - net                                     3           --             3            --
                                            --------     --------     ---------      --------

INCOME BEFORE INCOME TAXES                   100,446       98,213       186,143       228,896
   Income taxes                               34,241       33,412        63,899        77,666
                                            --------     --------     ---------      --------

INCOME BEFORE EXTRAORDINARY CHARGE            66,205       64,801       122,244       151,230
   Extraordinary charge                           --           --          (462)           --
                                            --------     --------     ---------      --------

NET INCOME                                  $ 66,205     $ 64,801     $ 121,782      $151,230
                                            ========     ========     =========      ========
</TABLE>


Per share data is omitted since the Company's common stock is 100% owned by GTE
Corporation (GTE).

See Notes to Condensed Financial Statements.




                                       1
<PAGE>   3


GTE Southwest Incorporated

MANAGEMENT'S DISCUSSION AND ANALYSIS OF FINANCIAL CONDITION
AND RESULTS OF OPERATIONS

(Dollars in Millions)

RESULTS OF OPERATIONS

<TABLE>
<CAPTION>
                                                     Three Months Ended                    Six Months Ended
                                                          June 30,                             June 30,
                                              ---------------------------------    ---------------------------------
                                                  1998               1997              1998               1997
                                              --------------     --------------    --------------    ---------------
<S>                                               <C>                <C>               <C>                <C>      
         Net income                               $    66.2          $    64.8         $   121.8          $   151.2
</TABLE>

Net income for the six months ended June 30, 1998 included an after-tax
extraordinary charge of $0.5. Excluding this charge, net income grew by 2% or
$1.4 during the three months ended June 30, 1998, compared to the same period in
1997, and year-to-date net income declined 19% or $29 below the first six months
of 1997. Second quarter net income increased primarily due to growth in revenues
from local services, network access services, and other services and sales,
partially offset by lower toll service revenues and higher operating costs and
expenses. Year-to-date net income decreased due to higher operating costs and
expenses, partially offset by an increase in revenues.

REVENUES AND SALES

<TABLE>
<CAPTION>
                                        Three Months Ended      Six Months Ended
                                             June 30,                 June 30,
                                        -------------------     -------------------
                                         1998        1997        1998        1997
                                        -------     -------     -------     -------
<S>                                     <C>         <C>         <C>         <C>    
         Local services                 $ 179.5     $ 154.6     $ 353.7     $ 313.4
         Network access services          183.8       171.5       349.8       329.8
         Toll services                     22.0        35.5        46.8        76.1
         Other services and sales          68.9        49.7       127.9       109.7
                                        -------     -------     -------     -------

           Total revenues and sales     $ 454.2     $ 411.3     $ 878.2     $ 829.0
</TABLE>

Total revenues and sales increased 10% or $42.9 and 6% or $49.2 for the three
and six months ended June 30, 1998, respectively, compared to the same periods
in 1997.

Local service revenues increased 16% or $24.9 and 13% or $40.3 for the three and
six months ended June 30, 1998, respectively, compared to the same periods in
1997. Growth in access lines of 6% during both the three months ended June 30,
1998, and on a year-to-date basis, generated additional revenues of $2.8 and
$6.8 from basic local services, and $5.7 and $7.8 from CentraNet(R) services
compared to the same periods for 1997, respectively. Growth in revenues from
enhanced services, such as caller ID, automatic call return/redial and other
SmartCall(R) and CLASS services, contributed $6.6 and $9.8, respectively, for
the three and six month periods ended June 30, 1998, as compared to the same
periods in 1997. Additionally, amortization of the reserve previously
established for potential refunds related to the 1989 Texas rate case resulted
in increases for the three and six month periods of $3.8 and $7.6, respectively.





                                       2
<PAGE>   4
GTE Southwest Incorporated

MANAGEMENT'S DISCUSSION AND ANALYSIS OF FINANCIAL CONDITION
AND RESULTS OF OPERATIONS (CONTINUED)

Network access service revenues grew 7% or $12.3 and 6% or $20 for the three and
six months ended June 30, 1998, respectively, compared to the same periods in
1997. A 10% increase in minutes of use for both the three and six months ended
June 30, 1998 generated additional access revenues of $10.6 and $20.7,
respectively. Special access revenues, driven by growing demand for increased
bandwidth by Internet Service Providers (ISPs) and other high capacity users,
increased by $6.9 and $12.7 for the three and six month periods, respectively.
Offsetting these increases were decreases of $7.3 and $14.6 for the three and
six month periods, respectively, resulting from the impact of interstate access
rate reductions from the 1997 Federal Communications Commission (FCC) price cap.

Toll service revenues decreased 38% or $13.5 and 39% or $29.3 for the three and
six months ended June 30, 1998, compared to the same periods in 1997. These
decreases were primarily due to a decline in domestic toll volumes, resulting
from the effects of intraLATA (local access transport area) toll competition,
including 10XXX and 1+ presubscription.

Other services and sales revenues increased 39% or $19.2 and 17% or $18.2 for
the three and six months ended June 30, 1998 compared to the same periods in
1997. For the three month and six month periods ended June 30, 1998, revenues
increased by $1.9 and $3.3 resulting from the FCC's order increasing payphone
compensation from interexchange carriers, and $2.5 and $3.5 in billing and
collection services, respectively. Additionally, for both the three and six
month periods ended June 30, 1998, compared to the same periods in 1997, voice
messaging increased $1.1, database 800 services increased $3.6 and Tele-Go(R)
revenue grew by $2.6.

OPERATING COSTS AND EXPENSES

<TABLE>
<CAPTION>
                                                                        
                                           Three Months Ended       Six Months Ended
                                                 June 30,                June 30,
                                           -------------------     -------------------
                                             1998        1997        1998        1997
                                           -------     -------     -------     -------
<S>                                        <C>         <C>         <C>         <C>    
   Cost of services and sales              $ 168.2     $ 144.4     $ 329.8     $ 273.4
   Selling, general and administrative        77.0        64.5       144.6       115.0
   Depreciation and amortization              91.0        91.1       183.5       184.1
                                           -------     -------     -------     -------

    Total operating costs and expenses     $ 336.2     $ 300.0     $ 657.9     $ 572.5
</TABLE>

Total operating costs and expenses increased 12% or $36.2 and 15% or $85.4 for
the three and six month periods ended June 30, 1998, respectively, compared to
the same periods in 1997. These increases were due in part to increases in
switch software right-to-use fees of $9.6 and $13.2, and increases in operating
taxes of $8.6 and $6.8, respectively. Selling and marketing expenses increased
$5.4 and $10.3 as a result of continued efforts to stimulate sales of enhanced
services and in response to the increasingly competitive environment. Labor and
benefit costs increased $4.7 and $21.6 for the three and six months ended June
30, 1998, respectively, compared to the same periods in 1997, to support access
line 



                                       3
<PAGE>   5

GTE Southwest Incorporated

MANAGEMENT'S DISCUSSION AND ANALYSIS OF FINANCIAL CONDITION
AND RESULTS OF OPERATIONS (CONTINUED)

growth and customer demand for products and services. Customer care expenses
increased $3.6 and $16.7 for the three and six month periods as a result of
growth in access lines and expansion of daily operating hours of the customer
care centers.

OTHER EXPENSES

<TABLE>
<CAPTION>
                             Three Months Ended      Six Months Ended
                                  June 30,                  June 30,
                             -------------------     -------------------
                              1998        1997        1998        1997
                             -------     -------     -------     -------
<S>                          <C>         <C>         <C>         <C>    
    Interest - net           $  17.6     $  13.1     $  34.1     $  27.6
    Income taxes                34.2        33.4        63.9        77.7
    Extraordinary charge          --          --         0.5          --
</TABLE>

Interest-net increased 34% or $4.5 for the three months and 24% or $6.5 for the
six months ended June 30, 1998, compared to the same periods in 1997. These
increases were primarily due to higher average short-term debt levels.

Income taxes increased 2% or $0.8 in the second quarter of 1998 and decreased
18% or $13.8 during the six months ended June 30, 1998, compared to the same
periods in 1997. The second quarter increase was primarily due to an increase
in pre-tax income. The year-to-date decrease was primarily due to a decrease in
pre-tax income partially offset by other tax adjustments.

During the first quarter of 1998, the Company recorded an after-tax
extraordinary charge of $0.5, reflecting premiums paid on the redemption of
high-coupon debt prior to stated maturity.

CAPITAL RESOURCES AND LIQUIDITY

Management believes that the Company has adequate internal and external
resources available to meet ongoing operating requirements for construction of
new plant, modernization of facilities and payment of dividends. The Company
generally funds its construction program from operations, although external
financing is available. Short-term financings can be obtained through borrowings
from the Company's parent, GTE, or GTE Funding Incorporated, an affiliate of the
Company. The Company participates with other affiliates in a $1,500, 364-day
syndicated line of credit.

The Company's principal source of funds during the first six months of 1998 was
cash from operations of $260.4 compared to $229.8 for the same period in 1997.
The year-to-year increase in cash from operations primarily reflects a decrease
in working capital requirements, partially offset by a decline in results from
operations.

The Company's capital expenditures during the first six months of 1998 were
$248.3 compared to $209.4 for the same period in 1997. The 1998 expenditures 





                                       4
<PAGE>   6

GTE Southwest Incorporated

MANAGEMENT'S DISCUSSION AND ANALYSIS OF FINANCIAL CONDITION
AND RESULTS OF OPERATIONS (CONTINUED)

reflect the Company's continued access line growth and the modernization of
current facilities to mitigate Internet congestion. Although the capital
expenditures during the first six months of 1998 were higher than the same
period in 1997, the overall anticipated capital expenditures for 1998 are
expected to be comparable to the total capital expenditures incurred during 
1997.

Net cash used in financing activities was $6.6 during the first half of 1998
compared to $19.2 for the same period in 1997. This included dividend payments
of $80.3 in the first six months of 1998 compared to $125 for the same period in
1997. Short-term financings, including the net change in affiliate notes,
decreased $30.3 compared to an increase of $136.2 for the same period in 1997.
In January 1998, the Company issued $150 of 6.23% debentures to repay short-term
borrowings incurred to finance the Company's construction program and for
general corporate purposes. Additionally, during the first six months of 1998,
the Company paid a total of $42.3 for the retirement of debt and preferred stock
compared to $30.3 for the same period in 1997. Additionally, the Company
recognized an interest rate hedge loss of approximately $2.6 on the settlement
of forward contracts related to the January 1998 debt issuances. The loss is
being amortized over the life of the associated refinanced debt.

In its April 2, 1998 filing on Form 8-K, GTE stated that because the MCI
shareholders had accepted a competing offer, GTE's offer for MCI was no longer
outstanding. As a result, the Company and GTE were removed from "Credit Watch"
by all rating agencies. The Company believes that its present investment grade
credit rating provides ready access to the capital markets at reasonable rates
and provides the Company with the financial flexibility necessary to pursue
growth opportunities as they arise.

OTHER MATTERS

Federal Regulatory Developments

The Company filed interstate access revisions during 1997 that became effective
June 3, 1997 and July 1, 1997. Overall, these filings resulted in a net annual
price reduction of $25.5. On December 1, 1997, the FCC issued an order to file
revised access rates effective January 1, 1998, which resulted in additional
interstate access charge reductions of $3.1 annually. In 1997, the FCC also
ordered significant changes that altered the structure of access charges
collected by the Company, effective January 1, 1998. Generally, the FCC reduced
and restructured the per minute charges paid by long distance carriers and
implemented new per line charges. The FCC also created an access charge
structure that resulted in different access charges for residential primary and
secondary lines and single line and multi-line business access lines. In



                                       5
<PAGE>   7
GTE Southwest Incorporated

MANAGEMENT'S DISCUSSION AND ANALYSIS OF FINANCIAL CONDITION
AND RESULTS OF OPERATIONS (CONTINUED)

aggregate, the annual reductions in usage sensitive access charges of $10.8 
paid by long distance carriers were offset by $10.8 of new per line charges 
and the charges paid by end-users. Effective July 1, 1998, access charges 
were further reduced by $25.8 annually in compliance with FCC requirements 
to restate the impacts of access charge reform.

In May 1997, the FCC released a major decision relating to implementation of the
Telecommunications Act's provision on universal service. GTE and numerous 
other parties have challenged the FCC's decision before the U.S. Court of
Appeals for the Fifth Circuit on the grounds that the FCC did not follow the
requirements of the Telecommunications Act to develop a sufficient, explicit and
competitively neutral universal service program. Oral argument is not expected
until mid-September 1998 at the earliest, with a final decision to be issued by
mid-1999.

On March 9, 1998, the FCC adopted a Memorandum Opinion and Order (MO&O)
clarifying the payphone-specific coding digit requirements set forth in the
previous payphone orders and granting limited waivers of the requirement that
local exchange carriers (LECs) provide payphone-specific coding digits to
payphone service providers (PSPs), and that PSPs provide payphone-specific
coding digits from their payphones to interexchange carriers (IXCs), before PSPs
can receive per-call compensation from IXCs for subscriber 800 and access code
calls. GTE was granted waivers through 1998 in this order for Flex-ANI (Flexible
Automatic Number Identification) implementation due to technical problems
associated with switch conversions. 

On April 3, 1998, the FCC issued another MO&O which granted the IXCs a waiver of
the per-call compensation requirement so that they may pay per-phone instead of
per-call compensation for the payphones for which the FCC had granted technology
waivers. GTE will receive per-phone compensation under this waiver until the
Flex-ANI capable offices are activated. Qualifying payphone calls from Flex-ANI
switches will then be eligible for per-call compensation rather than per-phone. 

In a related court case between MCI and the FCC, the U.S. Court of Appeals,
District of Columbia Circuit, upheld the fundamental premise underlying the
FCC's approach to setting the per-call compensation rate for uncompensated
payphone calls, thereby supporting the ordered per-call compensation rate noted
in the March 9th order. At the same time, however, the Court held that the FCC
had failed to clearly explain its methodology on the development of that same
per-call compensation rate. The Court remanded this portion back to the FCC.


                                       6
<PAGE>   8
GTE Southwest Incorporated

MANAGEMENT'S DISCUSSION AND ANALYSIS OF FINANCIAL CONDITION
AND RESULTS OF OPERATIONS (CONTINUED)

State Regulatory Developments

A lawsuit was filed previously against the Company for allegedly violating the
Texas Debt Collection Practices Act (the Act) by failing to include a "street
address" on the Company's disconnection notices. The Company's disconnection
notices provide a post office box for remittance of payment and a toll-free
number for inquiries, but do not provide a physical street address. On September
1, 1995, an amendment to the Act became effective which provides that a post
office box, street address or telephone number on delinquency notices meets the
requirements of the Act. The Court granted the Company's motion to defer the
case to the Texas Public Utilities Commission (TPUC); however, the plaintiff's 
counsel challenged the constitutionality of the legislative amendment. 
On June 10, 1998, the case was dismissed.

RECENT DEVELOPMENTS

On July 27, 1998, GTE and Bell Atlantic entered into a merger agreement
providing for the combination of the two companies in a merger of equals
transaction. Under terms of the definitive agreement, which was unanimously
approved by the board of directors of both companies, GTE shareholders will
receive 1.22 shares of Bell Atlantic stock for each GTE share they own. The
merger is expected to be accounted for as a pooling of interests, is subject to
shareholder and regulatory approval, and is expected to be completed during the
second half of 1999. For additional information regarding the merger, refer to
the Form 8-K filed by GTE dated July 27, 1998.

In April 1998, GTE announced a series of actions designed to further sharpen
its strategic focus and improve its competitive position by repositioning
non-strategic properties and reducing costs. GTE expects to generate after-tax
proceeds of $2,000 to $3,000 by selling non-strategic or under-performing
operations and plans to reduce annual costs by more that $500 through improved
efficiencies and productivity while it continues to invest in new high-growth
opportunities. The impact of this announcement on the Company is unknown at
this time. GTE's management is currently assessing its options, and as
decisions are finalized regarding the sale of non-strategic operations and cost
reductions, the Company could be affected.


                                       7
<PAGE>   9
GTE Southwest Incorporated
CONDENSED BALANCE SHEETS

<TABLE>
<CAPTION>
                                                                June 30,       December 31,
                                                                 1998             1997
                                                              -----------      -----------
                                                                  (Thousands of Dollars)
<S>                                                           <C>              <C>        
ASSETS
Current assets:
  Cash and cash equivalents                                   $    29,725      $    24,282
  Receivables, less allowances of $22,812 and $21,203             364,311          359,879
  Inventories and supplies                                         29,358           24,032
  Prepaid insurance                                                14,662            1,587
  Prepaid taxes and other                                          19,552           58,379
                                                              -----------      -----------

    Total current assets                                          457,608          468,159
                                                              -----------      -----------

Property, plant and equipment, at cost                          5,639,199        5,418,247
  Accumulated depreciation                                     (3,462,025)      (3,317,186)
                                                              -----------      -----------

    Total property, plant and equipment, net                    2,177,174        2,101,061
                                                              -----------      -----------

Prepaid pension costs and other assets                            186,556          162,995
                                                              -----------      -----------

Total assets                                                  $ 2,821,338      $ 2,732,215
                                                              ===========      ===========

LIABILITIES AND SHAREHOLDERS' EQUITY 
  Current liabilities:
  Short-term obligations, including current maturities        $         8      $       313
  Notes payable to affiliates                                     173,189           42,826
  Accounts payable                                                153,005          204,648
  Taxes payable                                                    39,792           37,027
  Accrued interest                                                 13,645           10,103
  Accrued payroll costs                                            40,934           33,252
  Dividends payable                                                56,763           45,458
  Other                                                           123,743          106,267
                                                              -----------      -----------

    Total current liabilities                                     601,079          479,894
                                                              -----------      -----------

  Long-term debt                                                  942,740          984,955
  Deferred income taxes                                           181,361          174,745
  Employee pension plans and other liabilities                    213,417          238,556
                                                              -----------      -----------

    Total liabilities                                           1,938,597        1,878,150
                                                              -----------      -----------

Preferred stock, subject to mandatory redemption                       --            1,510
                                                              -----------      -----------

Shareholders' equity:
  Preferred stock                                                   7,600            7,600
  Common stock (6,500,000 shares issued)                          650,000          650,000
  Additional paid-in capital                                       48,751           48,751
  Retained earnings                                               176,390          146,204
                                                              -----------      -----------

    Total shareholders' equity                                    882,741          852,555
                                                              -----------      -----------

Total liabilities and shareholders' equity                    $ 2,821,338      $ 2,732,215
                                                              ===========      ===========
</TABLE>

See Notes to Condensed Financial Statements.



                                       8
<PAGE>   10

GTE Southwest Incorporated
CONDENSED STATEMENTS OF CASH FLOWS

<TABLE>
<CAPTION>
                                                                                 Six Months Ended
                                                                                     June 30,
                                                                              ------------------------
                                                                                1998           1997
                                                                              ---------      ---------
                                                                                (Thousands of Dollars)
<S>                                                                           <C>            <C>      
OPERATIONS
  Income before extraordinary charge                                          $ 122,244      $ 151,230
  Adjustments to reconcile income before extraordinary charge to net cash
  from operations:
    Depreciation and amortization                                               183,506        184,162
    Deferred income taxes                                                        11,535          2,925
    Provision for uncollectible accounts                                         19,124         15,290
    Changes in current assets and current liabilities                           (32,082)      (125,789)
    Other - net                                                                 (43,964)         1,961
                                                                              ---------      ---------

    Net cash from operations                                                    260,363        229,779
                                                                              ---------      ---------

INVESTING
  Capital expenditures                                                         (248,299)      (209,439)
                                                                              ---------      ---------

    Net cash used in investing                                                 (248,299)      (209,439)
                                                                              ---------      ---------

FINANCING
  Long-term debt issued                                                         148,868             --
  Long-term debt and preferred stock retired,
    including premiums paid on early retirement                                 (42,318)       (30,336)
  Dividends                                                                     (80,253)      (125,000)
  Increase (decrease) in short-term obligations, excluding
    current maturities                                                          (30,282)       136,150
  Other - net                                                                    (2,636)            --
                                                                              ---------      ---------

    Net cash used in financing                                                   (6,621)       (19,186)
                                                                              ---------      ---------

Increase in cash and cash equivalents                                             5,443          1,154

Cash and cash equivalents:
  Beginning of period                                                            24,282         23,134
                                                                              ---------      ---------

  End of period                                                               $  29,725      $  24,288
                                                                              =========      =========
</TABLE>


See Notes to Condensed Financial Statements.



                                       9
<PAGE>   11





GTE Southwest Incorporated
NOTES TO CONDENSED FINANCIAL STATEMENTS


(1)      BASIS OF PRESENTATION:

         The unaudited Condensed Financial Statements included herein have been
         prepared by the Company pursuant to the rules and regulations of the
         Securities and Exchange Commission (SEC). Certain information and
         footnote disclosures normally included in financial statements prepared
         in accordance with generally accepted accounting principles have been
         condensed or omitted pursuant to such rules and regulations. However,
         in the opinion of management of the Company, the Condensed Financial
         Statements include all adjustments, which consist only of normal
         recurring accruals, necessary to present fairly the financial
         information for such periods. These Condensed Financial Statements
         should be read in conjunction with the financial statements and the
         notes thereto included in the Company's 1997 Annual Report on Form
         10-K.

         Reclassifications of prior year data have been made, where appropriate,
         to conform to the 1998 presentation.

(2)      EXTRAORDINARY CHARGE:

         During the first quarter of 1998, the Company recorded an after-tax
         extraordinary charge of $0.5 million, reflecting premiums paid on the
         redemption of high-coupon debt prior to stated maturity.

(3)      DEBT:

         In January 1998, the Company issued $150 million of 6.23% Series D
         Debentures, due 2007. The net proceeds were applied toward the
         repayment of short-term borrowings incurred for the purpose of
         financing the Company's construction program and for general corporate
         purposes.

(4)      RECENT ACCOUNTING PRONOUNCEMENTS:

         Computer Software

         In March 1998, the American Institute of Certified Public Accountants
         issued Statement of Position 98-1, "Accounting for the Costs of
         Computer Software Developed or Obtained for Internal Use" (SOP 98-1).
         SOP 98-1 defines internal-use software and establishes accounting
         standards for the costs of such software. The Company is currently
         assessing the impact of adopting SOP 98-1, and intends to implement as
         of January 1, 1999.

         Derivative Instruments and Hedging Activities

         In June 1998, the Financial Accounting Standards Board issued Statement
         of Financial Accounting Standards No. 133, "Accounting for Derivative





                                       10
<PAGE>   12
GTE Southwest Incorporated
NOTES TO CONDENSED FINANCIAL STATEMENTS (CONTINUED)

         Instruments and Hedging Activities"(FAS 133). FAS 133 establishes
         accounting and reporting standards for derivative instruments,
         including certain derivative instruments embedded in other contracts,
         and for hedging activities. The Company has not yet assessed the impact
         of adopting FAS 133.




                                       11
<PAGE>   13
GTE Southwest Incorporated

PART II. OTHER INFORMATION

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

    (a)  Exhibits required by Item 601 of Regulation S-K.

         12   Statement re: Calculation of the Ratio of Earnings to Fixed
              Charges

         27   Financial Data Schedule

    (b) The Company filed no reports on Form 8-K during the second quarter of
        1998.




                                       12
<PAGE>   14

                                    SIGNATURE

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.


                                                GTE Southwest Incorporated
                                           ------------------------------------
                                                      (Registrant)

Date:     August 14, 1998                        /s/ Stephen L. Shore       
     ---------------------                 ------------------------------------
                                                     Stephen L. Shore
                                                       Controller
                                              (Principal Accounting Officer)



                                       13
<PAGE>   15

                                 EXHIBIT INDEX

<TABLE>
<CAPTION>
  Exhibit
   Number                              Description
-----------  -------------------------------------------------------------------
<S>          <C>
    12       Statement re: Calculation of the Ratio of Earnings to Fixed Charges

    27       Financial Data Schedule
</TABLE>