<PAGE>   1

                                   FORM 10-Q

                       SECURITIES AND EXCHANGE COMMISSION
                            Washington, D.C.  20549

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

                    For the quarter ended September 30, 1996

                          Commission File No. 0-10810

                              KIEWIT ROYALTY TRUST
             (Exact name of Registrant as specified in its charter)


           Nebraska                                     47-6131402
------------------------------------     ---------------------------------------
(State or other jurisdiction of            (I.R.S. Employer Identification No.)
 incorporation or organization)


                        First Bank, National Association
                               1700 Farnam Street
                               Omaha, Nebraska  68102
                    ----------------------------------------
                    (Address of Principal Executive Offices)

                                  (402) 348-6275
                ------------------------------------------------
                (Registrant's telephone no. including area code)


         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
                                               -----     -----

                    APPLICABLE ONLY TO CORPORATE REGISTRANTS

         Indicate the number of shares outstanding of each of the registrant's
classes of common stock, as of the latest practicable date.

         As of September 30, 1996, there were 12,633,432 Units of Beneficial
Interest of the registrant outstanding.
<PAGE>   2
                        PART I - FINANCIAL INFORMATION.

ITEM 1.  FINANCIAL STATEMENTS.

                              KIEWIT ROYALTY TRUST
                STATEMENT OF ASSETS, LIABILITY AND TRUST CORPUS

                 as of September 30, 1996 and December 31, 1995


<TABLE>
<CAPTION>
ASSETS                                                            1996                        1995
------                                                      --------------               -------------- 
<S>                                                          <C>                          <C>
Cash and short-term investments                              $   2,993,802                 $    162,011

Net royalty and overriding
royalty interests in coal
leases:

Estimated fair market value
at date of transfer to Trust                                 $  73,878,000                 $ 73,878,000

Allowance to reduce carrying
value to Peter Kiewit Sons'
Inc.'s historical book value                                   (73,710,183)                 (73,710,183)
                                                             --------------                ------------

                                                             $     167,817                 $    167,817

Less accumulated amortization                                      (75,439)                     (70,897)


Net royalty and overriding
royalty interests in coal
leases                                                       $      92,378                 $     96,920
                                                             -------------                 ------------

Total Assets                                                 $   3,086,180                 $    258,931
                                                             =============                 ============

LIABILITY AND TRUST CORPUS
--------------------------

Distributions payable to
Unit Holders                                                 $   2,993,802                 $    162,011

Trust corpus: 12,633,432
units of beneficial interest
authorized and outstanding                                   $      92,378                 $     96,920
                                                             -------------                 ------------

Total Liability and Trust Corpus                             $   3,086,180                 $    258,931
                                                             =============                 ============
</TABLE>


                  The accompanying notes are an integral part
                          of the financial statements
<PAGE>   3
                              KIEWIT ROYALTY TRUST


                       STATEMENT OF DISTRIBUTABLE INCOME

     For the Three Months and Nine Months Ended September 30, 1996 and 1995


<TABLE>
<CAPTION>
                                        Three Months Ended                          Nine Months Ended
                                             September 30                             September 30
                                  -----------------------------------       -----------------------------------

                                         1996             1995                     1996              1995
                                        -----            -----                    -----              ----
<S>                                  <C>              <C>                      <C>              <C>
Royalty Income                       $2,978,007        $3,405,049              $5,518,364        $7,313,800

Interest income                      $   25,436        $   32,990              $   56,805        $   87,629

Trust expenses                           (9,641)          (11,952)                (39,113)          (29,339)
                                     ----------        ----------              ----------        ----------

Distributable
Income                               $2,993,802        $3,426,087              $5,536,056        $7,372,090
                                     ==========        ==========              ==========        ==========

Distributable Income
per unit (12,633,432 units)          $  .236975        $  .271192              $  .438207        $  .583538
</TABLE>


                 See Accompanying Notes to Financial Statements





                                     - 2 -
<PAGE>   4
                              KIEWIT ROYALTY TRUST

                      STATEMENT OF CHANGES IN TRUST CORPUS

             For the Nine Months Ended September 30, 1996 and 1995


<TABLE>
<CAPTION>
                                                       1996                        1995
                                                -----------------           -----------------
<S>                                                <C>                          <C>
Trust Corpus as of
   January 1                                       $    96,920                  $   108,822

Amortization of
   royalty interest                                     (4,542)                     (10,000)

Distributable Income                                 5,536,056                    7,372,090

Distribution to Unit
   Holders                                          (5,536,056)                  (7,372,090)
                                                   -----------                  -----------

Trust Corpus as of
   September 30                                    $    92,378                  $    98,822
                                                   ===========                  ===========
</TABLE>



                 See Accompanying Notes to Financial Statements





                                     - 3 -
<PAGE>   5
                              KIEWIT ROYALTY TRUST

                         Notes to Financial Statements
                 as of September 30, 1996 and December 31, 1995

BASIS OF PRESENTATION

                 The accompanying unaudited financial statements have been
prepared in accordance with the instructions for Form 10-Q and do not
necessarily include all of the information and footnotes required by generally
accepted accounting principles for complete financial statements.  In the
Trustee's opinion, all adjustments necessary for a fair presentation have been
included.  For further information, refer to the financial statements and
footnotes included in the Trust's annual report on Form 10-K for the year ended
December 31, 1995.

SUMMARY OF SIGNIFICANT ACCOUNTING POLICIES

                 The accompanying unaudited financial statements have been
prepared on the following basis:

                 (a)  The royalty income recorded for a month is the amount
                      computed and paid by the lease holder to the Trustee for
                      such month.

                 (b)  Trust administration expenses are recorded in the month
                      they accrue.

This basis for reporting royalty income is thought to be the most meaningful
because distributions to the Unit Holders for a month are based on net cash
receipts for such month.  However, these statements differ from financial
statements prepared in accordance with generally accepted accounting principles
because, under such principles, royalty income for a month would be based on
production for such month without regard to when calculated or received.  In
addition, amortization of the net royalty and overriding royalty interests,
which is calculated on a units-of-production basis by lease, is charged
directly to trust corpus, since such amount does not affect distributable
income.





                                     - 4 -
<PAGE>   6
ITEM 2. MANAGEMENT'S DISCUSSION AND ANALYSIS OF FINANCIAL CONDITION AND RESULTS
OF OPERATIONS.

        a.       MATERIAL CHANGES IN FINANCIAL CONDITION.

                 Kiewit Royalty Trust is a royalty trust with royalty and
overriding royalty interests in certain coal leases.  The Trust was formed for
the purposes of (1) administering the income received from such coal leases and
(2) distributing such income (together with interest earned thereon less
payment of or provision for obligations) to the holders of the Units of
Beneficial Interest.

        b.       MATERIAL CHANGES IN RESULTS OF OPERATIONS.

                 During the nine months ended September 30, 1996, the Trust
received a total of $5,518,364 of royalty and overriding royalty payments;
during the three months ended September 30, it received a total of $2,978,007
of such payments.  The following schedule reflects the royalty and overriding
royalty amounts received by the Trust from each mine.
<TABLE>
<CAPTION>
 Mine                              Three Months Ended                Nine Months Ended
 ----                                 September 30                     September 30
                               ---------------------------     -----------------------------
                                    1996          1995                1996           1995
                                    ----          ----                ----           ----
 <S>                             <C>          <C>                 <C>           <C>
 Decker                          $2,139,744   $2,338,528          $4,475,066    $5,644,098
 Spring Creek                       829,191      913,096             879,191       913,096
 Black Butte                             69      144,277             152,095       638,937
 Big Horn                             9,003        9,148              12,012       117,699
                                 ----------   ----------          ----------    ----------

                                 $2,978,007   $3,405,049          $5,518,364    $7,313,800
                                 ==========   ==========          ==========    ==========
</TABLE>

                 i.       DECKER MINE

                 The amount of royalties and overriding royalties received by
the Trust with respect to the Decker Mine decreased to $4,475,066 in the nine
months ended September 30, 1996 compared to $5,644,098 during the same period
in 1995.  For the third quarter of 1996, the amounts received decreased to
$2,139,744 compared to $2,338,528 during the third quarter of 1995.  These
variations in receipts during the nine months and three months ended September
30, 1996 were due to changes in the relative amounts of coal mined under leases
bearing high and low overriding royalty rates per ton, which are a normal
result of the execution of a mining plan encompassing several coal leases
bearing different royalty rates.





                                     - 5 -
<PAGE>   7
                 ii.      SPRING CREEK MINE

                 Royalties received from the Spring Creek Mine decreased from
$913,096 during the nine months ended September 30, 1995 to $879,191 during the
corresponding period in 1996.  The Trust received $829,191 in the third quarter
of 1996, compared to $913,096 during the third quarter of 1995.  This decrease
reflects decreased production from the applicable lease.  Royalties from the
Spring Creek Mine are typically paid by the mine operators on an annual basis
during the second half of the calendar year.

                 iii.     BLACK BUTTE MINE

                 The Trust received $152,095 in royalty and overriding royalty
amounts from the Black Butte Mine during the nine months ended September 30,
1996, a decrease from the $638,937 received during the nine months ended
September 30, 1995.  The Trust received $69 during the third quarter of 1996,
as compared to receipts of $144,277 during the third quarter of 1995.  The
decrease in royalties received during the nine months ended September 30, 1996
and the third quarter of 1996 as compared to the corresponding periods of 1995
reflects decreased sales from the Black Butte Mine as well as the fact that
Federal Lease number W-6266 was renewed effective April 1, 1996 and the Trust
no longer receives an overriding royalty on coal produced after March 31, 1996
as explained below.

                 Lease number W-6266 provides that the terms and conditions of
the lease are subject to "reasonable readjustment" effective on April 1, 1996.
At that time, the royalty rate payable to the United States was increased to
12-1/2%, which is the currently prevailing federal royalty rate.  Because of
the cap on the amount of the overriding royalty payable to the Trust with
respect to this lease, the increased royalty rate has effectively eliminated
further payments to the Trust with respect to this lease.

                 iv.      BIG HORN MINE

                 Overall royalties received from the Big Horn Mine decreased to
$12,012 during the nine months ended September 30, 1996 from $117,669 in 1995,
and decreased to $9,003 in the third quarter of 1996 from $9,148 in the third
quarter of 1995.  The decrease in the first nine months of 1996 reflects
decreased production from the applicable leases.  The Trustee anticipates that
there will be minimal production at the Big Horn Mine in the future.





                                     - 6 -
<PAGE>   8
                          PART II - OTHER INFORMATION.

ITEM 1.          LEGAL PROCEEDINGS.

                 There are no material pending legal proceedings to which the
Trust is a party or of which any of its property is the subject.

ITEM 6.          EXHIBITS AND REPORTS ON FORM 8-K.

                 (a)      Exhibits.

                          27.1     Financial Data Schedule.

                 (b)      No reports on Form 8-K were filed during the quarter
                          for which this report is filed.





                                     - 7 -
<PAGE>   9
                                   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.




                                 KIEWIT ROYALTY TRUST
                                       (Registrant)

                                 By: First Bank, National Association
                                     its capacity as Trustee and not
                                     in its individual capacity or
                                     otherwise
                                     
                                     
                                     
                                     By:  /s/   Susan K. Rosburg
                                         ---------------------------
                                         Susan K. Rosburg
                                         Trust Officer
                                     


Dated:  November 8, 1996