<PAGE>   1
                                  UNITED STATES
                       SECURITIES AND EXCHANGE COMMISSION
                           WASHINGTON, D.C. 20549-1004

                                   FORM 10-Q/A

(Mark One)

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

                For the quarterly period ended September 30, 1998

                                       OR

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


                         Commission file number 1-13916

                       UNION PACIFIC RESOURCES GROUP INC.
             (Exact name of registrant as specified in its charter)

              UTAH                                        13-2647483
(State or other jurisdiction of             (I.R.S. Employer Identification No.)
 incorporation or organization)

                       777 MAIN STREET, FORT WORTH, TEXAS
                    (Address of principal executive offices)

                                      76102
                                   (Zip Code)

                                 (817) 321-6000
              (Registrant's telephone number, 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
     -----          ----- 

     As of October 31, 1998, there were 251,009,284 shares of the registrant's
common stock outstanding.



<PAGE>   2


The purpose of this amendment is to file Exhibits 10.1, 10.2, 10.3, and 10.4
which were not included on the Registrant's Form 10-Q for the quarter ended
September 30, 1998, filed November 9, 1998.

The undersigned registrant hereby amends the following item of its Quarterly
Report on Form 10-Q for the quarter ended September 30, 1998.

PART II.  OTHER INFORMATION

ITEM 6.  EXHIBITS AND REPORTS ON FORM 8-K

(a)     EXHIBITS

        Exhibits not previously filed with the Quarterly Report on Form 10-Q for
the quarter ended September 30, 1998, filed November 9, 1998, are designated by
an asterisk (*) and are filed herewith.

*10.1    U.S. $1,000,000,000 364-Day Competitive Advance/Revolving Credit
         Agreement, dated as of October 27, 1998, among Union Pacific Resources
         Group Inc. and Chase Bank of Texas, N.A., as administrative agent and
         the banks named therein.

*10.2    U.S. $750,000,000 364-Day Competitive Advance/Revolving Credit
         Agreement, dated as of October 27, 1998, among Union Pacific Resources
         Group Inc. and Chase Bank of Texas, N.A., as administrative agent and
         the banks named therein.

*10.3    U.S. $750,000,000 Five-Year Competitive Advance/Revolving Credit
         Agreement, dated as of October 27, 1998, among Union Pacific Resources
         Group Inc. and Chase Bank of Texas, N.A., as administrative agent, The
         Chase Manhattan Bank of Canada, as Canadian sub-agent and the banks
         named therein.

*10.4    Form of Agreement relating to Change in Control by and between Union
         Pacific Resources Group Inc. and Thomas R. Blank, approved by the
         Compensation and Corporate Governance Committee of the Board of
         Directors on July 13, 1998.

11       Computation of earnings per share. (Exhibit 11 to Quarterly Report on
         Form 10-Q for the quarter ended September 30, 1998, filed November 9,
         1998.)

12       Computation of ratio of earnings to fixed charges. (Exhibit 12 to
         Quarterly Report on Form 10-Q for the quarter ended September 30, 1998,
         filed November 9, 1998.)

15       Awareness letter of Arthur Andersen LLP dated November 6, 1998.
         (Exhibit 15 to Quarterly Report on Form 10-Q for the quarter ended
         September 30, 1998, filed November 9, 1998.)

27       Financial data schedule. (Exhibit 27 to Quarterly Report on Form 10-Q
         for the quarter ended September 30, 1998, filed November 9, 1998.)

 (b)     REPORTS ON FORM 8-K

        None.


                                      - 2 -
<PAGE>   3


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.



Dated: November 12, 1998




                                    UNION PACIFIC RESOURCES GROUP INC.
                                    (Registrant)


                                    /s/ Morris B. Smith
                                    --------------------------------------------
                                    Morris B. Smith,
                                    Vice President and Chief Financial Officer
                                    (Chief Financial Officer and
                                      Duly Authorized Officer)


                                     - 3 -
<PAGE>   4


                       UNION PACIFIC RESOURCES GROUP INC.

                                  EXHIBIT INDEX


<TABLE>
<CAPTION>
Exhibit No.                                Description
-----------                                -----------
<S>              <C>                                                                     
*10.1            U.S. $1,000,000,000 364-Day Competitive Advance/Revolving Credit        
                 Agreement, dated as of October 27, 1998, among Union Pacific Resources  
                 Group Inc. and Chase Bank of Texas, N.A., as administrative agent and   
                 the banks named therein.                                                
                                                                                         
*10.2            U.S. $750,000,000 364-Day Competitive Advance/Revolving Credit          
                 Agreement, dated as of October 27, 1998, among Union Pacific Resources  
                 Group Inc. and Chase Bank of Texas, N.A., as administrative agent and   
                 the banks named therein.                                                
                                                                                         
*10.3            U.S. $750,000,000 Five-Year Competitive Advance/Revolving Credit        
                 Agreement, dated as of October 27, 1998, among Union Pacific Resources  
                 Group Inc. and Chase Bank of Texas, N.A., as administrative agent, The  
                 Chase Manhattan Bank of Canada, as Canadian sub-agent and the banks     
                 named therein.                                                          
                                                                                         
*10.4            Form of Agreement relating to Change in Control by and between Union    
                 Pacific Resources Group Inc. and Thomas R. Blank, approved by the       
                 Compensation and Corporate Governance Committee of the Board of         
                 Directors on July 13, 1998.                                             
                                                                                         
11               Computation of earnings per share. (Exhibit 11 to Quarterly Report on   
                 Form 10-Q for the quarter ended September 30, 1998, filed November 9,   
                 1998.)                                                                  
                                                                                         
12               Computation of ratio of earnings to fixed charges. (Exhibit 12 to       
                 Quarterly Report on Form 10-Q for the quarter ended September 30, 1998, 
                 filed November 9, 1998.)                                                
                                                                                         
15               Awareness letter of Arthur Andersen LLP dated November 6, 1998.         
                 (Exhibit 15 to Quarterly Report on Form 10-Q for the quarter ended      
                 September 30, 1998, filed November 9, 1998.)                            
                                                                                         
27               Financial data schedule. (Exhibit 27 to Quarterly Report on Form 10-Q   
                 for the quarter ended September 30, 1998, filed November 9, 1998.)      


                 * Filed Herewith
</TABLE>


                                     - 4 -