<PAGE>   1
                                   FORM 10-Q


                                 UNITED STATES
                       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, 1997

                          Commission File No. 0-10810

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


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


                               Trust Division
                       U.S. Bank National Association
                           d/b/a First Bank, N.A.
                             1700 Farnam Street
                           Omaha, Nebraska  68102
                   --------------------------------------
                  (Address of Principal Executive Offices)

                               (402) 348-6000
           ------------------------------------------------------
              (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, 1997, 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, LIABILITIES AND TRUST CORPUS

               as of September 30, 1997 and December 31, 1996

<TABLE>
<CAPTION>
ASSETS                                                     1997                       1996
------                                                     ----                       ----
<S>                                                   <C>                      <C>
Cash equivalents                                      $   3,247,172             $   244,268

Royalty and overriding
royalty interests in coal
leases                                                      167,817                 167,817

Less accumulated amortization                               (81,788)                (76,921)
                                                      -------------             -----------

Net royalty and overriding
royalty interests in coal leases                             86,029                  90,896
                                                      -------------             -----------

Total Assets                                          $   3,333,201             $   335,164
                                                      =============             ===========

LIABILITIES AND TRUST CORPUS
----------------------------

Distribution payable to unit holders                  $   3,247,172             $   244,268

Trust corpus: 12,633,432 units of beneficial
interest authorized and outstanding                          86,029                  90,896
                                                      -------------             -----------

Total Liabilities and Trust Corpus                    $   3,333,201             $   335,164
                                                      =============             ===========
</TABLE>


                  The accompanying notes are an integral part
                          of the financial statements





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<PAGE>   3
                              KIEWIT ROYALTY TRUST


                       STATEMENT OF DISTRIBUTABLE INCOME

          For the Three Months and Nine Months Ended September 30, 1997 and 1996


<TABLE>
<CAPTION>
                                Three Months Ended              Nine Months Ended
                                   September 30                   September 30   
                          ---------------------------      ----------------------------
                              1997             1996            1997             1996   
                          ----------       ----------       ---------        ----------
<S>                        <C>             <C>              <C>              <C>
Royalty income             $3,229,866      $2,978,007       $5,318,310       $5,518,364

Interest income                27,739          25,436           49,577           56,805

Trust expenses                (10,433)         (9,641)         (37,962)         (39,113)
                          -----------      ----------       ----------       ----------

Distributable income       $3,247,172      $2,993,802       $5,329,925       $5,536,056

Distributable
  income per unit
  (12,633,432 Units
  Outstanding)             $ .2570301      $ .2369746       $ .4218905       $ .4382068
</TABLE>



                      STATEMENT OF CHANGES IN TRUST CORPUS

            For the Nine Months Ended September 30, 1997 and 1996

<TABLE>
<CAPTION>
                                                 1997                             1996     
                                             -----------                      -------------
<S>                                        <C>                               <C>
Trust corpus as of January 1               $    90,896                       $     96,920

Amortization of royalty interests               (4,867)                            (4,542)

Distributable income                         5,329,925                          5,536,056

Distribution to unit holders                (5,329,925)                        (5,536,056)
                                           -----------                       ------------

Trust corpus as of September 30            $    86,029                       $     92,378 
                                           ===========                       ============
</TABLE>



                See Accompanying Notes to Financial Statements

                                       



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<PAGE>   4
                              KIEWIT ROYALTY TRUST

                         Notes to Financial Statements
                as of September 30, 1997 and December 31, 1996

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, 1996.

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.





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<PAGE>   5
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, 1997, the Trust
received a total of $5,318,310 of royalty and overriding royalty payments;
during the three months ended September 30, it received a total of $3,229,866
of such payments.  The following schedule reflects the royalty and overriding
royalty amounts received by the Trust from each mine.

<TABLE>
<CAPTION>
                                     Three Months Ended                 Nine Months Ended
                 Mine                   September 30                       September 30
                 ----              -----------------------           -------------------------
                                     1997           1996               1997            1996
                                     ----           ----               ----            ----
        <S>                        <C>            <C>                <C>            <C>
        Decker                    $2,346,807      $2,139,744         $4,420,919     $4,475,066
        
        Spring Creek                 872,941         829,191            872,941        879,191
        
        Black Butte                       -               69               (274)       152,095
        
        Big Horn                      10,118           9,003             24,724         12,012
                                  -----------    -----------        -----------     ----------
        
                                  $3,229,866      $2,978,007         $5,318,310     $5,518,364
                                  ===========    ===========        ===========     ==========
</TABLE>

             i.     DECKER MINE.

        The amount of royalties and overriding royalties received by the Trust
with respect to the Decker Mine decreased to $4,420,919 in the nine months
ended September 30, 1997 compared to $4,475,066 during the same period in 1996.
For the third quarter of 1997, the amounts received increased to $2,346,807
compared to $2,139,744 during the third quarter of 1996.  These variations in
receipts during the nine months and three months ended September 30, 1997 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>   6
             ii.     SPRING CREEK MINE.

                 Royalties received from the Spring Creek Mine decreased from
  $879,191 during the nine months ended September 30, 1996 to $872,941 during
  the corresponding period in 1997.  The Trust received $872,941 in the third
  quarter of 1997 compared to $829,191 during the same period in 1996 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 paid Black Butte Mine $274 during the first nine months of
1997, as compared to receiving a royalty of $152,095 during the first nine
months of 1996, and received no royalty during the three months ended September
30, 1997, as compared to receiving a royalty of $69 during the three months
ended September 30, 1996.  The $274 payment relates to a revision in the
royalties for the first quarter of 1996.  The decrease in royalties received
during the first nine months and third quarter of 1997 as compared to the
corresponding periods of 1996 reflects 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 increased to $24,724
during the nine months ended September 30, 1997 from $12,012 in 1996, and
increased to $10,118 in the third quarter of 1997 from 9,003 in the third
quarter of 1996. The increase in the first nine months of 1997 reflects
increased production from the applicable leases. The Trustee anticipates that
there will be minimal production at the Big Horn Mine in the future.





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<PAGE>   7
                          PART II - OTHER INFORMATION.

ITEM 1. LEGAL PROCEEDINGS.

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

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

        (a)      Exhibits

        4.1      Kiewit Royalty Trust Indenture dated May 17, 1982, as amended
                 June 9, 1982 and June 23, 1982 (filed as Exhibit 1 to the
                 Trust's Form 10 filed with the Securities and Exchange
                 Commission on December 23, 1982, and incorporated herein by
                 reference).

        4.2      Order dated September 23, 1994, of the County Court of Douglas
                 County, Nebraska (filed as Exhibit 2 to the Trust's Form 10-Q
                 filed with the Securities and Exchange Commission on November
                 14, 1994, and incorporated herein by reference).

        27.1     Financial Data Schedule.

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





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<PAGE>   8
                                   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:  U. S. Bank National Association
                         d/b/a First Bank, N.A. in its capacity as
                         Trustee and not in its individual capacity or otherwise
                          
                          
                                                By:   /s/ Susan K. Rosburg
                                                      --------------------
                                                           Susan K. Rosburg
                                                           Trust Officer

Dated:  November 7, 1997





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