<PAGE>   1


                                    FORM 10-K

                                  UNITED STATES
                       SECURITIES AND EXCHANGE COMMISSION
                             Washington, D.C. 20549

                   ANNUAL REPORT PURSUANT TO SECTION 13 OF THE
                         SECURITIES EXCHANGE ACT OF 1934

                   For the fiscal year ended December 31, 1998

                         Commission file number 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)

                                 Trust Division
                         U. S. Bank National Association
                               1700 Farnam Street
                              Omaha, Nebraska 68102
                    ----------------------------------------
                    (Address of principal executive offices)

                                 (402) 348-6000
                    ----------------------------------------
              (Registrant's telephone number, including area code)

<TABLE>
<S>                                                           <C>
Securities registered pursuant to Section 12(b) of the Act:          None
                                                            ---------------------
Securities registered pursuant to Section 12(g) of the Act:     Units of Beneficial Interest
                                                            -------------------------------------
                                                                      (Title of class)
</TABLE>

              Indicate by check mark whether the registrant (1) has filed all
reports required 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 report(s)), and (2) has been subject to such filing
requirements for the past 90 days. Yes X . No   .
                                      ---    ---

              Indicate by check mark if disclosure of delinquent filers pursuant
to Item 405 of Regulation S-K is not contained herein, and will not be
contained, to the best of registrant's knowledge, in definitive proxy or
information statement incorporated by reference in Part III of this Form 10-K or
any amendment to this Form 10-K. Yes X . No   .
                                    ---    ---

              There currently is no market for the Units of Beneficial Interest
of the registrant held by nonaffiliates of the registrant. Therefore, the
aggregate market value of the Units is not available.

              As of March 15, 1999, there were 12,633,432 Units of Beneficial
Interest of the registrant outstanding.


<PAGE>   2


                                TABLE OF CONTENTS

<TABLE>
<CAPTION>
                                                                            Page
                                                                            ----
<S>                                                                          <C>
Item 1.  Business............................................................. 1

         (a)  General Development of Business................................. 1

         (b)  Financial Information about Industry Segments................... 1

         (c)  Narrative Description of Business............................... 2

         (d)  Financial Information about Operations.......................... 3

Item 2.  Properties........................................................... 3

         (a)  Producing Leases................................................ 5

         (b)  Non-Producing Leases............................................ 9

Item 3.  Legal Proceedings.................................................... 9

Item 4.  Submission of Matters to a Vote of Security
                     Holders.................................................. 9

Item 5.  Market for Registrant's Common Equity and
                     Related Stockholder Matters.............................. 9

         (a)  Market Information.............................................. 9

         (b)  Holders.........................................................10

         (c)  Dividends.......................................................10

Item 6.  Selected Financial Data..............................................12

Item 7.  Management's Discussion and Analysis of
                     Financial Condition and Results of Operations............12

         (a)         Decker Mine .............................................13

         (b)         Black Butte Mine.........................................13

         (c)         Spring Creek Mine........................................14

         (d)         Big Horn Mine............................................14

         (e)         Trust Expenses...........................................14

         (f)         Year 2000 Issue .........................................13
</TABLE>


                                        i
<PAGE>   3


<TABLE>
<S>                                                                         <C>
Item 7A. Quantitative and Qualitative Disclosures about Material Risks........15

Item 8.  Financial Statements and Supplementary Data..........................15

         (a)  Financial Statements............................................15

         (b)  Supplementary Data..............................................23

Item 9.  Changes in and Disagreements With Accountants
           on Accounting and Financial Disclosure.............................23

Item 10. Directors and Executive Officers of the
                     Registrant...............................................23

Item 11. Executive Compensation...............................................23

Item 12. Security Ownership of Certain Beneficial
                     Owners and Management....................................23

         (a)         Security Ownership of Certain Beneficial
                     Owners...................................................23

         (b)  Security Ownership of Management................................23

         (c)  Changes in Control..............................................23

Item 13. Certain Relationships and Related Transactions.......................24

         (a)  Transactions with Management and Others.........................24

         (b)  Certain Business Relationships..................................24

         (c)  Indebtedness of Management......................................24

         (d)  Transactions with Promoters.....................................24

Item 14. Exhibits, Financial Statement Schedules, and
                     Reports on Form 8-K......................................24

         (a)  Financial Statements............................................24

         (b)  Reports on Form 8-K.............................................24

         (c)  Exhibits........................................................24

         (d) Separate Financial Statement Schedules...........................25

Signatures....................................................................26

Exhibit Index.................................................................27
</TABLE>


                                       ii
<PAGE>   4


Item 1. BUSINESS.

              (a)    GENERAL DEVELOPMENT OF BUSINESS. Kiewit Royalty Trust
(hereinafter referred to as the "Trust") is a trust organized under the laws of
the State of Nebraska. The Trust was created under a Trust Indenture dated May
17, 1982, which subsequently was amended as of June 9, 1982, June 23, 1982, and
by a court order dated September 23, 1994. A copy of the Trust Indenture is
attached to the Form 10 filed by the Trust on December 23, 1982, and is
incorporated herein by reference. A copy of the Order of the County Court of
Douglas County, Nebraska, dated September 23, 1994, amending the Trust Indenture
is attached to the Form 10-Q filed by the Trust on November 14, 1994, and is
incorporated herein by reference.

              The Trust was created by Level 3 Communications, Inc., a Delaware
corporation, formerly Peter Kiewit Sons', Inc. (hereinafter referred to as
"Level 3"). It was organized to provide an efficient, orderly and practical
means for the administration of income received from certain royalty and
overriding royalty interests*/ in certain coal leases. The royalty and
overriding royalty interests that the Trust owns were conveyed to the Trust by
Level 3 effective June 28, 1982, pursuant to conveyance documents that gave the
Trust legal title to the property interests conveyed. Ownership interests in the
Trust are represented by 12,633,432 units of beneficial interest (hereinafter
referred to as "Units"). On June 23, 1982, the Units were distributed pro rata
to holders of Level 3's Class B and Class C common stock, as of June 10, 1982,
who were citizens of the United States.

              The Trust has no active plan of business operation and is a purely
ministerial trust. The Trust Indenture currently provides that all available
income, after paying or making provisions for liabilities and obligations, is to
be distributed to holders of Units (hereinafter referred to as "Unit Holders")
during the months of January, April, July, and October of each year. The trustee
of the Trust is U.S. Bank National Association, Omaha, Nebraska, which is a
wholly owned subsidiary of U.S. Bancorp, a registered bank holding company.

              (b)    FINANCIAL INFORMATION ABOUT INDUSTRY SEGMENTS. The Trust
receives its income from only one industry segment. Financial information for
that industry segment appears in Item 8, below.

--------

*/   When the owner of mineral rights executes a lease entitling the lessee to
develop, mine, and sell the minerals, the lessee takes an "operating interest"
and the owner may retain a "royalty interest." A royalty interest is a right to
receive a specified amount per ton or a specified portion of the value of the
total production of the property, free of the expense of development and
operation. An "overriding royalty interest," which is similar to a royalty
interest, is sometimes retained by the lessee of the mineral rights upon the
lessee's assignment of the lease. Payment of an overriding royalty is generally
subject to payment of the royalty.


<PAGE>   5


              (c)    NARRATIVE DESCRIPTION OF BUSINESS. The Trust owns three (3)
royalty interests and sixteen (16) overriding royalty interests relating to
leases in four coal mining areas in Montana and Wyoming. The royalty and
overriding royalty interests transferred to the Trust previously had been owned
by various wholly owned Level 3 subsidiaries, and by Montana Royalty Company,
Ltd., a partnership among three wholly owned Level 3 subsidiaries and Resource
Development Co., Inc., a Washington state corporation.

              The Trust is administered by officers and employees of the
Trustee, but there are no specific persons employed by the Trustee having the
full-time duty of administering the Trust. Under the Trust Indenture, the basic
function of the Trustee is to collect income from the Trust's properties, to pay
out of the Trust's income and assets all expenses, charges, and obligations, and
to pay remaining cash to Unit Holders on a quarterly basis. The Trustee also is
obligated to make annual financial reports to Unit Holders, to file all
fiduciary income tax returns, and to prepare, execute, and deliver certificates
of beneficial interest to the Unit Holders. The Trustee is obligated, subject to
the terms of the Trust Indenture, to use its best judgment in good faith in all
matters relating to the Trust and Trust properties.

              The Trustee is authorized and required to use the money it
receives to pay all liabilities of the Trust, including but not limited to all
services as Trustee, and the compensation of geologists, engineers, accountants,
attorneys, or the professional expert persons that the Trustee may, in its
discretion, employ in the administration of the Trust. With respect to any
liability that is contingent or uncertain in amount or that otherwise is not
currently due, the Trustee has the discretion to establish cash reserves for the
payment thereof.

              All available net income of the Trust will be distributed pro rata
on a quarterly basis to Unit Holders. During any period between distributions to
Unit Holders, the Trustee may invest any cash being held as a reserve for
liabilities or for distribution in (i) time deposits of the Trustee Bank; (ii)
any open-ended management type investment company or investment trust registered
pursuant to the Investment Company Act of 1940 (provided that such investment
matures on or before the next succeeding distribution date and is held until
maturity); or (iii) trust-quality fixed net asset money market funds that have
total assets of $100,000,000 or more and consist solely of direct obligations of
the U.S. Government and/or next-business day repurchase agreements fully
collateralized by direct obligations of the U.S. Government.


                                        2
<PAGE>   6


              The Trust Indenture grants to the Trustee only such rights and
powers as are necessary to achieve the purposes of the Trust. The Trust
Indenture prohibits the Trustee from entering into or engaging in any business
or commercial activity of any kind or from using any portion of the assets of
the Trust to acquire any coal lease, royalty, or mineral interest. The Trustee
may sell Trust properties only as authorized by a vote of a majority-in-interest
of Unit Holders, except that the Trustee may sell Trust properties upon the
termination of the Trust without a vote of Unit Holders. Any sale of Trust
properties must be for cash, and the Trustee is obligated to distribute the
available net proceeds of any such sale pro rata to Unit Holders.

              The Trust is irrevocable, but it may be terminated by (i) three
successive fiscal years in which net revenue is less than $1,000,000 per year;
(ii) a vote in favor of termination by a majority-in-interest of Unit Holders;
or (iii) operation of the provisions of the Trust Indenture intended to permit
the Trust to comply with the rule against perpetuities. Upon the termination of
the Trust, the Trustee will continue to act in such capacity until all assets of
the Trust are distributed. The Trustee will sell all Trust properties for cash
in one or more sales and, after satisfying all expenses, claims and liabilities
and establishing adequate reserves, if necessary, for the payment of contingent
liabilities, will distribute the remaining proceeds of such sales according to
the respective interests and rights of Unit Holders.

              (d)    FINANCIAL INFORMATION ABOUT OPERATIONS. During 1998, the
Trust received gross royalty income of $5,790,542 for distribution to Unit
Holders. See Item 8, below.

Item 2. PROPERTIES.

              The Trust's properties consist of royalty and overriding royalty
interests in nineteen (19) coal leases in four mining areas located in the
States of Wyoming and Montana. All of these royalty and overriding royalty
interests were transferred to the Trust, as described in Item 1, above, by Level
3 and are subject to the provisions of the coal lease agreements under which
they were created.


                                        3
<PAGE>   7


              The royalty and overriding royalty interests transferred to the
Trust provide for the payment of either a specified amount per ton of coal
produced, or a fixed percentage of the value or price with respect to the coal
produced under the leases relating to these interests. The terms of these
royalty and overriding royalty interests vary considerably, as does the acreage
covered by the underlying coal leases, the total recoverable reserves on such
leases, and the recoverable reserves to be mined under current contracts.

              The remaining periods of the underlying coal leases as of December
31, 1998, including optional renewal periods, are such that, given the
productive capacity of the mines that are the subjects of the leases, the full
estimated total recoverable reserves could be extracted. However, it does not
appear likely that the estimated total recoverable reserves will in fact be
extracted. See "Properties -- Producing Leases -- Revised Production Estimates"
and "Management's Discussion and Analysis of Financial Condition and Results of
Operations," below. Failure to extract the total recoverable reserves or failure
to sell any portion of the coal extracted could adversely affect the royalties
payable to the Trust.

              The following chart sets forth the actual total amount of coal
production (including production under leases in which the Trust has no royalty
or overriding royalty interests) of the four mines to which the coal leases
pertain:

<TABLE>
<CAPTION>
                                                 -- Tons of Coal Produced --

                           1998             1997             1996             1995             1994
                           ----             ----             ----             ----             ----
<S>                     <C>              <C>              <C>              <C>              <C>
Decker Mine             10,475,407       11,873,448       10,990,492       10,277,584       10,514,777

Black Butte  Mine        2,667,718        1,928,894        1,838,293        2,240,962        4,029,771

Big Horn Mine               65,911           44,202           15,549           38,207           94,037

Spring Creek Mine       11,312,935        8,306,306        9,015,000        8,512,495        9,934,305
                        ----------       ----------       ----------       ----------       ----------


Total                   24,521,971       22,152,850       21,859,334       21,069,248       24,572,890
                        ==========       ==========       ==========       ==========       ==========
</TABLE>

              Set forth below is a summary by mine area of pertinent information
as of December 31, 1998, about each of the producing leases in which the Trust
has either royalty or overriding royalty interests.


                                        4
<PAGE>   8


        (a) PRODUCING LEASES.

          (i) DECKER MINE. Decker Coal Company ("Decker") operates this mine,
which is located in Big Horn County, Montana, approximately 20 miles north of
Sheridan, Wyoming. Decker is a joint venture between KCP Inc.*/ (a wholly owned
subsidiary of Level 3 Communications Inc. ) and Western Minerals, Inc. (a wholly
owned subsidiary of NERCO, Inc.). Each joint venturer owns a fifty percent (50%)
interest in the joint venture. The Decker Mine in its entirety includes
approximately 17,838 acres and has an annual productive capacity of 16,000,000
tons.

              The Trust owns overriding royalty interests in six (6) productive
leases at the Decker Mine. The terms of the Trust's overriding royalty interests
and the estimated total recoverable reserves of each lease are set forth in the
table below, of which the accompanying notes are an integral part:

<TABLE>
<CAPTION>
                                                                                                       Estimated
                                                                Terms of                               Total Recover-
                                                                Overriding                             able Reserves
Lease                          Lessor                           Royalties                                (in tons)
-----                          ------                           ---------                               -----------
<S>                            <C>                              <C>                                    <C>
M-073093                       United States                     5 cents per ton**/                     114,050,000

M-061685                       United States                    10 cents per ton**/                      26,519,000

M-057934                       United States                    10 cents per ton**/                      28,971,000

C-527-63***/                   Montana                          10 cents per ton****/                    10,717,000

C-531-65*****/                 Montana                           5 cents per ton****/                     9,113,000

C-823-66******/                Montana                           5 cents per ton****/                       - 0 -
                                                                                                        -----------

              Total Estimated Recoverable Reserves                                                      189,370,000
                                                                                                        ===========
</TABLE>

--------

*/   Kiewit Coal Properties Inc.'s name was changed to KCP Inc. on March 25,
1998.

**/   The Trust has an undivided one-half interest in a second overriding
royalty pertaining to this lease. By the terms of the assignment by which it was
created, this second overriding royalty, when added to all other overriding
royalties pertaining to the lease, may not exceed fifty percent (50%) of the
royalty payable to the lessor under the lease.

***/   This Lease was renewed effective November 13, 1993 and was assigned a new
lease number of C-1085-93.

****/   The Trust has an undivided one-half interest in a second overriding
royalty pertaining to this lease. By the terms of the assignment by which it was
created, this second overriding royalty, when added to the underlying royalty
pertaining to the lease, will be equal to the highest cumulative royalties being
paid in the States of Montana or Wyoming.

*****/   This Lease was renewed effective April 14, 1995 and was assigned a new
lease number of C-1087-95.

******/   This Lease was renewed effective June 2, 1996 and was assigned a new
lease number of C-1090-96.


                                        5
<PAGE>   9


              (ii) BLACK BUTTE MINE. Black Butte Coal Company ("Black Butte")
operates this mine in Sweetwater County, approximately 35 miles east of Rock
Springs, Wyoming. Black Butte is a joint venture between KCP Inc. and Bitter
Creek Coal Company (a wholly owned subsidiary of Union Pacific Resources Group
Inc.*/). The Black Butte Mine in its entirety includes approximately 50,220
acres and has an annual productive capacity of 6,000,000 tons.

              The Trust owns overriding royalty interests in two (2) productive
leases at the Black Butte Mine. The terms of the Trust's overriding royalty
interests and the estimated total recoverable reserves of each lease are set
forth in the table below, of which the accompanying note is an integral part:

<TABLE>
<CAPTION>
                                                                                                  Estimated              
                                                                   Terms of                     Total Recover-           
                                                                   Overriding                   able reserves            
Lease                    Lessor                                    Royalties                       (in tons)             
-----                    ------                                    ---------                       ---------             
<S>                      <C>                                       <C>                           <C>                     
W-6266                   United States                             50% of the                    3,853,000               
                                                                   royalty                                               
                                                                   payable to                                            
                                                                   the lessor                                            
                                                                                                                         
0-27475                  Wyoming                                   3% of the                                             
                                                                   gross output                  4,251,000               
                                                                                                 ---------               
                                                                                                                         
                         Total Estimated Recoverable Reserves                                    8,104,000               
                                                                                                 =========               
</TABLE>

              The Trust's overriding royalty from lease number W-6266 is further
limited to the difference between a specified amount per ton and the royalty per
ton payable to the lessor.**/


--------

*/   Union Pacific Resources Group Inc. was spun off with an I.P.O. on October
15, 1995 from Union Pacific Corporation.

**/   Total remaining reserves on lease W-6266 are 23,011,000 tons. However, due
to a renegotiation provision regarding the royalty payable under the lease and
the cap on the amount of the overriding royalty, the Trust no longer receives an
overriding royalty on coal produced after March 31, 1996. See "Management's
Discussion and Analysis of Financial Condition and Results of Operations."


                                        6
<PAGE>   10


              (iii) BIG HORN MINE. Big Horn Coal Company ("Big Horn") has
operated this mine, which is located approximately 5 miles north of Sheridan,
Wyoming, in Sheridan County. Big Horn is a wholly owned subsidiary of KCP Inc.
The Big Horn Mine in its entirety includes approximately 4,890 acres and has an
annual productive capacity of 3,000,000 tons. The Trust owns royalty interests
in three (3) productive leases at the Big Horn Mine.

              The terms of the Trust's royalty interests and the estimated total
recoverable reserves of each lease are set forth in the table below, of which
the accompanying notes are an integral part:

<TABLE>
<CAPTION>
                                                                                          Estimated
                                                                                            Total
                                                                                         Recoverable
                                                           Terms of                       reserves
Lease                        Lessor                        Royalties                      (in tons)
-----                        ------                        ---------                     -----------

<S>                          <C>                           <C>                           <C>
Hitson                       Whitney Holdings              12 1/2% of selling                413,000
Lease                        Corp. */   

Hitson-Schreibeis            Whitney Holdings              10 cents per ton                  761,000
Lease                        Corp.      

Flying V                     Whitney Holdings              10% of avg. gross
Lease                        Corp.                         sales price **/                   936,000
                                                                                             -------
                                       Total Estimated Recoverable Reserves                2,110,000
                                                                                           =========
</TABLE>

              The Trustee understands that Level 3 anticipates minimal
production from the Big Horn Mine in 1999 (and in future years) as a result of
the expiration of the primary coal sales contract at the end of 1988. See
"Management's Discussion and Analysis of Financial Condition and Results of
Operations," below.

--------

*/   Peter Kiewit Sons' Co.'s name was changed to Whitney Holdings Corp.
effective March 19, 1998. Whitney Holdings Corp. is a wholly-owned subsidiary of
PKS Information Services, Inc., which in turn is a wholly-owned subsidiary of
Level 3 Communications Inc.

**/   By the terms of the assignment by which it was created, the royalty
payable for this lease is 10% of the average gross sales price per ton or, if
greater, the highest royalty payable to the U.S. government for similar quality
coal mined in the State of Wyoming.


                                        7
<PAGE>   11


              (iv) SPRING CREEK MINE. Spring Creek Coal Company ("Spring Creek")
operates this mine, which is located in Big Horn County, Montana, approximately
25 miles north of Sheridan, Wyoming. Spring Creek is a subsidiary of NERCO, Inc.
The Spring Creek Mine in its entirety includes approximately 2,560 acres and has
an annual productive capacity of 12,000,000 tons.

              The Trust owns an overriding royalty interest in one productive
lease at the Spring Creek Mine. The terms of the overriding royalty interest and
the estimated total recoverable reserves of the lease are set out below:

<TABLE>
<CAPTION>
                                                                                  Estimated
                                                    Terms of                    Total Recover-
                                                   Overriding                   able reserves
Lease                    Lessor                     Royalties                     (in tons)
-----                    ------                     ---------                   -----------
<S>                      <C>                       <C>                          <C>
M-069782                 United States             10 cents per ton*/           65,028,000
                                                                                ==========
</TABLE>

              (v) REVISED PRODUCTION ESTIMATES. The numbers set forth in the
charts above in the column entitled "Estimated Total Recoverable Reserves"
reflect estimates made at the time of the formation of the Trust in 1982,
reduced to reflect the amount of coal actually extracted from the relevant
leases. As a result, certain of these numbers do not reflect current conditions
in the coal market. In light of recent reductions in the amounts of coal
purchased under existing coal contracts (based both upon elections by customers
to take the minimum quantities of coal permitted under the terms of such
agreements and upon amendments of such agreements) and current conditions in the
coal market, the amount of coal expected to be produced from such leases has
been significantly reduced. As of December 31, 1998, the Trustee understands
that the amounts of coal expected to be recovered from the relevant leases were
as follows:

<TABLE>
<CAPTION>
                        Lease                      Revised Estimate
                        -----                      ----------------
                  <S>                                <C>
                      M-073093                       11,274,000
                                                     ----------

                       W-6266                          - 0 -

                       0-27475                         - 0 -

                       Hitson                          - 0 -

                  Hitson-Schreibeis                    - 0 -

                      Flying V                         50,000
                                                       ------
</TABLE>

--------

*/   Under the terms of the lease, if the production royalty payable to the
United States is increased, then the overriding royalty will be recomputed to
equal 10.75% of such production royalty.


                                       8
<PAGE>   12


        (b) NON-PRODUCING LEASES. In addition to its interests in these
productive leases, the Trust has overriding royalty interests in three (3)
leases, containing 27,800,000 tons of total estimated recoverable coal reserves
from which no production is currently contemplated and in four (4) leases,
containing approximately 19,300,000 tons of coal, which are considered to be not
minable because of access, alluvial valley, or other problems.

Item 3. LEGAL PROCEEDINGS.

              None.

Item 4. SUBMISSION OF MATTERS TO A VOTE OF SECURITY HOLDERS.

              Not applicable.

Item 5. MARKET FOR REGISTRANT'S COMMON EQUITY AND RELATED
        STOCKHOLDER MATTERS.

              (a) MARKET INFORMATION. There is no established public trading
market for the Units. The Units have not been registered under the Securities
Act of 1933 ("1933 Act"), nor have they been registered under the securities
laws of any state. Accordingly, resales of the Units are subject to certain
restrictions on transferability.

              Under the 1933 Act, the Units should be treated as "restricted
securities." As such, resales of the Units are subject to certain restrictions
on transferability under the federal securities laws. Unit Holders should
consult with their own counsel regarding their ability to sell their Units.
However, under the Securities and Exchange Commission's Rule 144, a Unit Holder
who is not an "affiliate" */ of the Trust and has held his or her Units since
the creation of the Trust should be able to sell such Units without restriction.
Any Unit Holder who has acquired his or her Units since the creation of the
Trust should likewise be able to sell such Units without restriction so long as
at least two years have elapsed since such Units were owned by any affiliate of
the Trust. In this regard, it should also be noted that sales of the Units might
be made without compliance with Rule 144 pursuant to the less definite standards
of the so-called Section 4(1-1/2) exemption from the registration requirements
of the 1933 Act.

              None of the Units is subject to outstanding options or warrants to
purchase, and no securities are convertible into Units. Under the terms of the
Trust Indenture, the Trust may not issue additional Units.

--------

*/   Under Rule 144(a)(i), an "affiliate" of the Trust would be any person that
directly, or indirectly through one or more intermediaries, controls, or is
controlled by, or is under common control with, the Trust.


                                       9
<PAGE>   13


              (b) HOLDERS. The Units are the only class of security issued by
the Trust. The table below sets forth the approximate number of Unit Holders of
record on December 31, 1998:

<TABLE>
<CAPTION>
                                                    Approximate Number
                                                    ------------------
                  Title of Class                    of Unit Holders
                  --------------                    ---------------
                  <S>                               <C>
                  Units of Beneficial                     805
                                                          ===
                  Interest                              
</TABLE>

              (c) DIVIDENDS. The Trust pays no dividends since it is not a
corporation. Within ten (10) business days after the end of each calendar
quarter, however, the Trustee will distribute the Quarterly Distribution Amount
(as defined below) for the three preceding months, together with any
undistributed interest earned on each such amount to the payment date. This
distribution is made pro rata to Unit Holders of record on the last business day
for each such quarter (the "Quarterly Record Date").

              The Quarterly Distribution Amount distributed to each Unit Holder
is the excess, if any, of (i) the cash received during such quarter that is
attributable to the royalties and overriding royalties held by the Trust, plus
any decrease in any cash reserve theretofore established by the Trustee for the
payment of liabilities of the Trust, plus any other cash receipts of the Trust
during such quarter other than interest earned on the Quarterly Distribution
Amount for any other quarter that is earned before the actual distribution for
the fiscal quarter that includes that other quarter, over (ii) the liabilities
of the Trust paid during such quarter plus the amount of any cash reserve
established or increased by the Trustee for the payment of any future or
contingent liabilities of the Trust.

              The table below shows the aggregate Quarterly Distribution Amounts
(including interest) for each quarter during 1998 and 1997 and shows the date on
which such amounts were distributed:


                                       10
<PAGE>   14


<TABLE>
<CAPTION>
                                       1998
                                       ----

Quarter                     Date Dis-                --Distribution Amounts--
 Ended                      tributed              In Total               Per Unit
-------                     --------              --------               --------

<S>                         <C>                   <C>                    <C>     
March 31, 1998              04/13/98              $2,535,543             $.200701

June 30, 1998               07/10/98                 197,923              .015667

Sept. 30, 1998              10/09/98               2,897,099              .229320

Dec. 31, 1998               01/13/99                 163,236              .012921
                                                  ----------             --------
Total Distributed                                 $5,793,801             $.458609
                                                  ==========             ========
</TABLE>


<TABLE>
<CAPTION>
                                       1997
                                       ----

Quarter                     Date Dis-                --Distribution Amounts--
 Ended                      tributed              In Total               Per Unit
-------                     --------              --------               --------

<S>                         <C>                   <C>                    <C>     
March 31, 1997              04/11/97              $1,851,559             $.146560

June 30, 1997               07/10/97                 231,194              .018300

Sept. 30, 1997              10/10/97               3,247,172              .257030

Dec. 31, 1997               01/14/98                 180,832              .014314
                                                  ----------             --------
Total Distributed                                 $5,510,757             $.436204
                                                  ==========             ========
</TABLE>


                                       11
<PAGE>   15

Item 6. SELECTED FINANCIAL DATA.

        The table below sets forth selected financial data, drawn from the
Trust's audited financial statements, for each of the last five years.


<TABLE>
<CAPTION>
                                          Years Ended December 31,
                                          ------------------------

                            1998            1997           1996              1995             1994
                            ----            ----           ----              ----             ----

<S>                     <C>             <C>             <C>               <C>              <C>       
Royalty and             $5,846,421      $5,558,238      $5,829,963        $7,581,124       $7,873,846
Interest
Income

Received                  --------        --------        --------          --------           80,655*/
Escrowed
Funds

Amounts                   --------        --------        --------          --------         --------
Reserved
by Trustee

Trust                      (52,620)        (47,481)        (49,637)          (47,023)         (63,691)
Expenses                ----------      ----------      ----------        ----------       ----------

Distributable           $5,793,801      $5,510,757      $5,780,326        $7,534,101       $7,890,810
Income                  ==========      ==========      ==========        ==========       ==========

Distributable           $  .458609      $  .436204      $  .457542        $  .596362       $  .624597
Income Per Unit         ==========      ==========      ==========        ==========       ==========
(12,633,432
units)

Total Assets            $  232,351      $  263,038      $  335,164        $  258,931       $  507,440
                        ==========      ==========      ==========        ==========       ==========
</TABLE>


Item 7. MANAGEMENT'S DISCUSSION AND ANALYSIS OF FINANCIAL CONDITION AND RESULTS 
        OF OPERATIONS.

        Distributable income (the total amount of net royalty and overriding
royalty payments received from the various mines, increased by the amount of
interest earned and any other amounts received by the Trust and decreased by the
amount of Trust expenses) for 1998 was $5,793,801 compared to $5,510,757 for
1997.

--------

*/   This figure represents $80,538 paid by Black Butte to the Trust during the
fourth quarter of 1993 but reserved by the Trustee, plus accrued interest
thereon in the amount of $117 as of December 31, 1993.


                                       12
<PAGE>   16



            Distributable income (the total amount of net royalty and overriding
royalty payments received from the various mines, increased by the amount of
interest earned and any other amounts received by the Trust and decreased by the
amount of Trust expenses) for 1997 was $5,510,757 compared to $5,780,326 for
1996.

        The following schedule reflects the royalty and overriding royalty
payments received by the Trust in respect of leases at the following mines:

<TABLE>
<CAPTION>
         Mine                       1998                    1997                     1996
       --------                     ----                    ----                     ----

<S>                             <C>                      <C>                      <C>       
       Decker                   $4,689,836               $4,587,359               $4,707,364

       Black Butte                - 0 -                        (274)                 153,352

       Spring Creek                974,359                  872,942                  879,192

       Big Horn                    126,347                   40,156                   24,426
                                   -------               ----------               ----------

                                $5,790,542               $5,500,183               $5,764,334
                                ==========               ==========               ==========
</TABLE>

              (a) DECKER MINE. The amount of royalties and overriding royalties
received by the Trust with respect to the Decker Mine increased to $4,689,836 in
1998 from $4,587,359 in 1997. The amount of royalties and overriding royalties
received by the Trust with respect to the Decker Mine decreased to $4,587,359 in
1997 from $4,707,364 in 1996. These changes were the net result due to (i)
changes in the relative amounts of coal mined under leases bearing high and low
overriding royalty rates per ton, which were a normal result of the execution of
a mining plan encompassing several coal leases bearing different royalty rates,
and (ii) a lower average selling price for coal mined in 1998 resulting from the
expiration of a long-term coal contract which was replaced by several other
contracts.

              (b) BLACK BUTTE MINE. Royalties received by the Trust from the
Black Butte Mine was $0 in 1998 compared to ($274) in 1997. The $274 payment
relates to a revision in the royalties from the first quarter of 1996. 

              Royalties received by the Trust from the Black Butte Mine
decreased to ($274) in 1997 from $153,352 in 1996. This decrease is the result
of decreased sales of Black Butte Mine as well as the fact that Federal Lease
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.


                                       13
<PAGE>   17

              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 will be 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 will effectively eliminate further
payments to the Trust with respect to that lease.

              (c) SPRING CREEK MINE. Royalties received by the Trust with
respect to the Spring Creek Mine increased to $974,359 in 1998 from $872,942 in
1997. This increase reflects increased production under the applicable lease.
Royalties received from the Spring Creek Mine decreased to $872,942 during 1997
from $879,142 in 1996. The decrease reflects decreased production under the
applicable lease.

              (d) BIG HORN MINE. Royalties received by the Trust with respect to
the Big Horn Mine increased to $126,347 in 1998 from $40,156 in 1997. The
increase reflects increased production under the applicable lease. Royalties
received from the Big Horn Mine increased to $40,156 during 1997 from $24,426 in
1996. The increase reflects increased production under the applicable lease.

              (e) TRUST EXPENSES. Trust expenses increased to $52,620 in 1998
from $47,481 in 1997. The increase was primarily due to an increase in legal
and accounting expenses as well as certain administrative expenses.

              (f) YEAR 2000 ISSUE.

              The "Year 2000" computer problem has arisen because many computer
applications worldwide will not properly recognize the date change from December
31, 1999, to January 1, 2000, potentially causing production of erroneous data,
miscalculations, system failures and other operational problems.

              Since the Trust does not have any computer system of its own,
initiatives to address the Year 2000 issue has been undertaken by the Trustee,
U.S. Bank National Association, to evaluate the Year 2000 impact on its critical
computer hardware and software. The Trust does not incur any cost in the
Trustee's addressing of its Year 2000 problem. The Trustee has indicated to the
Trust that it has developed a strategic plan focusing on achieving Year 2000
compliance. Certain systems are being replaced, modified or reprogrammed to be
Year 2000 compliant. If necessary, new hardware and software is being purchased
to be Year 2000 compliant. Systems are being tested in an isolated environment
dedicated to Year 2000 testing. The Year 2000 project includes contingency plans
to mitigate potential delays or other problems, such as back-up solutions for
all mission-critical applications and


                                       14
<PAGE>   18


business continuation plans for significant vendors and other business partners.
The Year 2000 efforts of the Trustee and any related third parties are not
within the Trust's control, however, and their failure to remediate Year 2000
issues successfully could result in business disruption, increased operating
costs and increased credit risk for the Trust. At the present time, it is not
possible to determine whether any such events are likely to occur, or to
quantify any potential negative impact they may have on the Trust's future
results of operations and financial condition.

              Ultimately, the potential impact of the Year 2000 issue will
depend not only on the success of the corrective measures undertaken by the
Trustee, but also on the way in which the Year 2000 issue is addressed by
vendors, service providers, counterparties, utilities, governmental agencies and
other entities with which the Trustee and the Trust do business. These parties
are receiving communication from the Trustee to heighten their awareness of the
Year 2000 issue, to learn how the Trustee is addressing it and to evaluate any
likely impact on the Trustee and the Trust.

              The foregoing discussion regarding Year 2000 contains
forward-looking statements, which are based on management's best estimates
derived using various assumptions. These forward-looking statements involve
inherent risks and uncertainties, and actual results could differ materially
from those contemplated by such statements. Such material differences could
result in, among other things, business disruption, operational problems,
financial loss, legal liability and similar risks. 

Item 7A.QUANTITATIVE AND QUALITATIVE DISCLOSURES ABOUT MATERIAL RISKS.

              Not applicable

Item 8. FINANCIAL STATEMENTS AND SUPPLEMENTARY DATA.

              (a) FINANCIAL STATEMENTS. The following documents are filed as
part of the Trust's financial statements for the period from January 1, 1998 to
December 31, 1998:

              (1)    Report of Independent Accountants

              (2)    Statements of Assets, Liabilities and Trust Corpus

              (3)    Statements of Distributable Income and Statements of 
                     Changes in Trust Corpus

              (4)    Notes to Financial Statements


                                       15
<PAGE>   19




                              KIEWIT ROYALTY TRUST
                                     -------

                              FINANCIAL STATEMENTS
                        as of December 31, 1998 and 1997
                          and for the three years ended
                                December 31, 1998




<PAGE>   20


                           PRICEWATERHOUSECOOPERS LLP
                          a professional services firm



                        REPORT OF INDEPENDENT ACCOUNTANTS


The Trustee and Unit Holders
Kiewit Royalty Trust

We have audited the accompanying statements of assets, liabilities and trust
corpus of Kiewit Royalty Trust as of December 31, 1998 and 1997, and the related
statements of distributable income and changes in trust corpus for each of the
three years in the period ended December 31, 1998. These financial statements
are the responsibility of the Trustee. Our responsibility is to express an
opinion on these financial statements based on our audits.

We conducted our audits in accordance with generally accepted auditing
standards. Those standards require that we plan and perform the audit to obtain
reasonable assurance about whether the financial statements are free of material
misstatement. An audit includes examining, on a test basis, evidence supporting
the amounts and disclosures in the financial statements. An audit also includes
assessing the accounting principles used and significant estimates made by the
Trustee, as well as evaluating the overall financial statement presentation. We
believe that our audits provide a reasonable basis for our opinion.

As described in Note 1, the financial statements have been prepared on the basis
of accounting which differs in some respects from generally accepted accounting
principles. Accordingly, the accompanying financial statements are not intended
to present financial position and results of operations of Kiewit Royalty Trust
in conformity with generally accepted accounting principles.

In our opinion, the financial statements referred to above present fairly, in
all material respects, the assets, liabilities and trust corpus of Kiewit
Royalty Trust as of December 31, 1998 and 1997, and the distributable income and
changes in trust corpus for each of the three years in the period ended December
31, 1998, in conformity with the basis of accounting described in Note 1 to the
financial statements.

                        /s/  PricewaterhouseCoopers LLP

Omaha, Nebraska
March 15, 1999


                                       17
<PAGE>   21


                              KIEWIT ROYALTY TRUST
               STATEMENTS OF ASSETS, LIABILITIES AND TRUST CORPUS
                           December 31, 1998 and 1997
                                   ----------

<TABLE>
<CAPTION>
                ASSETS                                         1998             1997
                                                               ----             ----

<S>                                                           <C>              <C>     
Cash equivalents                                              $163,236         $180,832


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

  Less accumulated amortization                                (98,702)         (85,611)
                                                              --------         --------


                Net royalty and overriding                      69,115           82,206
                royalty interests in coal leases              --------         --------



Total Assets                                                  $232,351         $263,038
                                                              ========         ========



                LIABILITIES AND TRUST CORPUS

Distributions payable to unit holders                         $163,236         $180,832



Trust corpus:  12,633,432 units of beneficial                   69,115           82,206
  interest authorized and outstanding                         --------         --------

Total Liabilities and Trust Corpus                            $232,351         $263,038
                                                              ========         ========
</TABLE>


                  The accompanying notes are an integral part
                          of the financial statements.


                                       18
<PAGE>   22



                              KIEWIT ROYALTY TRUST
                       STATEMENTS OF DISTRIBUTABLE INCOME
                   for the three years ended December 31, 1998
                                   ----------

<TABLE>
<CAPTION>
                                            1998                      1997                  1996
                                            ----                      ----                  ----

<S>                                      <C>                      <C>                   <C>       
Royalty income                           $5,790,542               $5,500,183            $5,764,334



Interest income                              55,879                   58,055                65,629



Trust expenses                              (52,620)                 (47,481)              (49,637)
                                         ----------               ----------            ----------


Distributable income                     $5,793,801               $5,510,757            $5,780,326
                                         ==========               ==========            ==========


Distributable income per unit             $ .458609                $ .436204             $ .457542
                                          =========                =========             =========
</TABLE>


                     STATEMENTS OF CHANGES IN TRUST CORPUS
                  for the three years ended December 31, 1998
                                   ----------

<TABLE>
<CAPTION>
                                              1998                    1997                  1996
                                              ----                    ----                  ----

<S>                                      <C>                      <C>                   <C>       
Trust corpus, beginning of year            $ 82,206               $   90,896            $   96,920



Amortization of royalty interests           (13,091)                  (8,690)               (6,024)



Distributable income                      5,793,801                5,510,757             5,780,326



Distributions to unit holders            (5,793,801)              (5,510,757)           (5,780,326)
                                         ----------               ----------            ----------


Trust corpus, end of year                $   69,115               $   82,206            $   90,896
                                         ==========               ==========            ==========
</TABLE>



                  The accompanying notes are an integral part
                          of the financial statements.


                                       19
<PAGE>   23



                              KIEWIT ROYALTY TRUST
                          NOTES TO FINANCIAL STATEMENTS
                                   ----------

1.      Summary of Significant Accounting Policies and Basis of Accounting:

        (a)   Basis of Accounting:
              The financial statements of the Kiewit Royalty Trust (the Trust)
              are prepared on the following basis:

              (1)    The royalty income recorded for a month is the amount 
                     received from the lease holder for such month.

              (2)    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 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 royalty payments are
              received. In addition, amortization of the net royalty and
              overriding royalty interests, which is calculated on a
              units-of-production basis on a lease, is charged directly to trust
              corpus since such amount does not affect distributable income.

        (b)   Cash Equivalents:
              Cash equivalents consist of money market funds, which are recorded
              at cost plus interest.

2.      Trust Organization and Provisions:

        The Kiewit Royalty Trust was established on May 17, 1982. On June 28,
        1982, Level 3 Communications, Inc., formerly Peter Kiewit Sons', Inc.
        ("Level 3") conveyed to the Trust royalty and overriding royalty
        interests owned by Level 3's subsidiaries in certain coal properties in
        Montana and Wyoming.

        Units of beneficial interest (Units) in the Trust were distributed on
        June 23, 1982 to Level 3's Class B and Class C shareholders of record as
        of June 10, 1982 who were citizens of the United States. These
        shareholders received one Unit in the Trust for each share of Level 3
        stock held.


                                       20
<PAGE>   24

                              KIEWIT ROYALTY TRUST
                    NOTES TO FINANCIAL STATEMENTS, CONTINUED
                                   ----------


2.      Trust Organization and Provisions, Continued:

        FirsTier Bank, N.A., Omaha was Trustee for the Trust through February
        15, 1996. On February 16, 1996, FirsTier Bank merged with First Bank,
        National Association. On August 1, 1997 First Bank merged with U.S.
        Bank, a regional bank in the Pacific Northwest and changed its name to
        U.S. Bank National Association, who is now the Trustee for the Trust.
        The terms of the trust indenture provide, among other things, that:

        (a)   the Trust shall not engage in any business or investment activity
              of any kind or acquire any assets other than those initially 
              conveyed to the Trust;

        (b)   the Trustee may not sell all or any part of the royalty interests
              unless approved by a majority of Units outstanding, in which case
              the sale must be for cash and the proceeds promptly distributed;

        (c)   the Trustee may establish a cash reserve for the payment of any
              liability which is contingent or uncertain in amount;

        (d)   the Trustee will make cash distributions to the unit holders in
              January, April, July and October of each year as discussed in 
              Note 4; and 

        (e)   in September 1994, the Trust Indenture was amended to authorize 
              the Trustee to invest funds in government obligations, 
              government-secured obligations and funds registered pursuant to 
              the Investment Company Act of 1940. 

3.      Royalty and Overriding Royalty Interests:

        The cash received by the Trustee from the royalty interest will consist
        of a specified amount per ton or a specified fraction of the value of
        the total production of the property, free of the expense of development
        and operation.

        The initial carrying value of the royalty interests of $167,817
        represents Level 3's historical net book value at the date of the
        transfer to the Trust.

4.      Distributions to Unit Holders:

        The amounts to be distributed to unit holders (Quarterly Distribution
        Amount) are determined on a quarterly basis. The Quarterly Distribution
        Amount is the excess of (i) the cash received during the quarter which
        is attributable to royalties, plus any decrease in cash reserves, plus
        any other cash receipts of the Trust during the quarter over (ii) the
        liabilities of the Trust paid during the quarter, plus any increase in
        cash reserves. The Quarterly Distribution Amount is payable to unit
        holders of record as of the last business day of each quarter. The cash
        distributions are made quarterly within the first 10 business days of
        January, April, July and October.


                                       21
<PAGE>   25

                              KIEWIT ROYALTY TRUST
                    NOTES TO FINANCIAL STATEMENTS, CONTINUED
                                   ----------


5.      Income Taxes:

        Provision for federal and state income taxes has not been made in the
        financial statements since, in the opinion of legal counsel, the Trust
        should be treated as a "grantor trust" which is not a taxable entity.

6.      Summary of Quarterly Financial Data (Unaudited):

        The following is a summary of the unaudited quarterly financial
        information:

<TABLE>
<CAPTION>
                                                                                            Distributable
                                                      Net                                      Income and
                                                    Royalty           Distributable         Distributions
For the year ended December 31, 1998:               Income               Income                Per Unit
                                                   --------           -------------         -------------

<S>                                              <C>                     <C>                    <C>     
            March 31, 1998                       $2,534,970              $2,535,543              $.200701
            June 30, 1998                           203,430                 197,923               .015667
            September 30, 1998                    2,884,143               2,897,099               .229320
            December 31, 1998                       167,999                 163,236               .012921
                                                 ----------              ----------              --------

                                                 $5,790.542              $5,793,801              $.458609
                                                 ==========              ==========              ========

For the year ended December 31, 1997:
            March 31, 1997                       $1,850,105              $1,851,559             $ .146560
            June 30, 1997                           238,339                 231,194               .018300
            September 30, 1997                    3,229,866               3,247,172               .257030
            December 31, 1997                       181,873                 180,832               .014314
                                                  ---------              ----------               -------

                                                 $5,500,183              $5,510,757             $ .436204
                                                 ==========              ==========             =========
</TABLE>


                                       22
<PAGE>   26


              (b) SUPPLEMENTARY DATA. Not applicable.

Item 9. CHANGES IN AND DISAGREEMENTS WITH ACCOUNTANTS ON ACCOUNTING AND 
              FINANCIAL DISCLOSURE.

              Not Applicable.

Item 10.      DIRECTORS AND EXECUTIVE OFFICERS OF THE REGISTRANT.

              The Trust was created as a trust under the laws of the State of
Nebraska and its Indenture does not provide for the election of directors or
officers. U.S. Bank National Association serves as Trustee. See Item 1, above.

Item 11.      EXECUTIVE COMPENSATION.

              As stated in Item 10, above, the Trust has no directors and no
officers. During 1998, the Trust incurred $52,620 of administration expenses.

Item 12.      SECURITY OWNERSHIP OF CERTAIN BENEFICIAL OWNERS AND MANAGEMENT.

              (a) SECURITY OWNERSHIP OF CERTAIN BENEFICIAL OWNERS. The following
table sets forth the persons who, as of December 31, 1998, were known by the
Trust to be beneficial owners of more than five percent of the Units:

<TABLE>
<CAPTION>
                    Name and                 Amount and
                    Address of               Nature of
Title of            Beneficial               Beneficial             Percent of
 Class              Owner                    Ownership                Class
--------            ----------               ----------             ----------

<S>                 <C>                      <C>                      <C>  
Units of            Walter Scott, Jr.        800,000 Units            6.33%
Beneficial          1000 Kiewit Plaza
Interest            Omaha, NE  68131
</TABLE>

              (b) SECURITY OWNERSHIP OF MANAGEMENT. There are no executive
officers or directors of the Trust. See Item 10, above. As of December 31, 1998,
U.S. Bank National Association, Trustee, did not beneficially own any Units in
the Trust.

              (c) CHANGES IN CONTROL. As of December 31, 1998, the Trust had no
knowledge of any arrangements, the operation of which could, at a subsequent
date, result in a change of control of the Trust.


                                       23
<PAGE>   27

Item 13. CERTAIN RELATIONSHIPS AND RELATED TRANSACTIONS.

              (a) TRANSACTIONS WITH MANAGEMENT AND OTHERS. As stated in Item 10,
above, the Trust has no directors and no officers. During 1998, there were no
transactions to which the Trust was a party and in which any persons known to
the Trust to be the beneficial owners of more than five percent of the Units had
a direct or indirect material interest.

              (b) CERTAIN BUSINESS RELATIONSHIPS. There are no directors or
nominees for director of the Trust. See Item 10, above.

              (c) INDEBTEDNESS OF MANAGEMENT. As stated in Item 10, above, the
Trust has no directors and no officers.

              (d) TRANSACTIONS WITH PROMOTERS. Not applicable. 

Item 14.      EXHIBITS, FINANCIAL STATEMENT SCHEDULES, AND REPORTS ON FORM 8-K.

              (a)    (1) FINANCIAL STATEMENTS. See Item 8, above.

                     (2) FINANCIAL STATEMENT SCHEDULES. See Item 8, above, and 
                         Item 14(d), below. 

                     (3) EXHIBITS. See Item 14(c), below.

              (b) REPORTS ON FORM 8-K. The Trust did not file any reports on
Form 8-K during the quarter ended December 31, 1997.

              (c) EXHIBITS. The following exhibits are attached hereto and
incorporated by reference unless noted otherwise.

                     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.

                     99.1  Location Map of Coal Properties (filed as Exhibit 2
to the Trust's Form 10-K filed with the Securities and Exchange Commission on 
March 31, 1985, and incorporated herein by reference).

                                       24

<PAGE>   28

              (d) SEPARATE FINANCIAL STATEMENTS AND SCHEDULES. Not applicable.


                                       25
<PAGE>   29


                               S I G N A T U R E S

              Pursuant to the requirements of Section 13 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
                                 in its capacity as Trustee and not in its 
                                 individual capacity or otherwise


                                 By: /s/ Susan K. Rosburg
                                    -------------------------------------------
                                     Susan K. Rosburg
                                     Trust Officer

Date:  March 19, 1999

              Pursuant to the requirements of the Securities Exchange Act of
1934, this Annual Report on Form 10-K has been signed below by the following
persons on behalf of the Registrant and in the capacities and on the dates
indicated.

<TABLE>
<CAPTION>
            Name                       Capacity            Date
            ----                       --------            ----

<S>                                    <C>                 <C> 
U.S. Bank National Association         Trustee             March 19, 1999
</TABLE>



By: /s/ Susan K. Rosburg
   ----------------------
   Susan K. Rosburg
   Trust Officer


                                       26
<PAGE>   30

                                  EXHIBIT INDEX

<TABLE>
<CAPTION>
Exhibit                                                                                                           Page
-------                                                                                                           ----


<S>           <C>
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 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.

99.1          ***/ Location Map of Coal Properties (filed as Exhibit 2 to the Trust's Form 10-K filed with the
              Securities and Exchange Commission on March 31, 1985, and incorporated herein by reference).
</TABLE>

--------

*/   Appears at sequentially numbered page 35 in the Trust's Form 10, as
amended.

**/   Appears at sequentially numbered page 37 in the Trust's Form 10-Q filed on
November 14, 1994. 

***/   Appears at sequentially numbered page 36 in the Trust's Form 10-K filed
on March 31, 1985.


                                       27