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                                     FORM 4
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                UNITED STATES SECURITIES AND EXCHANGE COMMISSION
                             Washington, D.C. 20549


   
                  STATEMENT OF CHANGES IN BENEFICIAL OWNERSHIP
     Filed pursuant to Section 16(a) of the Securities Exchange Act of 1934,
         Section 17(a) of the Public Utility Holding Company Act of 1935
             or Section 30(f) of the Investment Company Act of 1940


/ /  Check  this  box if no  longer  subject  to  Section  16.  Form 4 or Form 5
     obligations may continue. See Instruction 1(b).
                           
  
                                                                              
                            (Print or Type Response)

                                                                                
1.   Name and Address of Reporting Person* 
  
     Hunt               Douglas            H. 
     ----------------------------------------------
     (Last)            (First)         (Middle)
     
     3900 Thanksgiving Tower, 1601 Elm Street
     ----------------------------------------------
                      (Street)  

     Dallas             Texas            75201 
     ----------------------------------------------  
     (City)            (State)          (Zip)


2.   Issuer Name and Ticker or Trading Symbol                                
                                                 
     Arch Coal, Inc. (ACI)                           
     ------------------------------------------------ 


3.   IRS or Social Security Number of Reporting Person (Voluntary)
    
     ------------------------       


4.   Statement for Month/Year

     5/1998
     ------------------------

                               
5.  If Amendment, Date of Original (Month/Year) 


     ------------------------


6.  Relationship of Reporting Person(s) to Issuer (Check all applicable)

     / X / Director      /   / Officer (Give Title)                   
                                                   ---------------    
    /   / 10% Owner      /   / Other (Specify)                        
                                                   ---------------    
 
7.  Individual or Joint/Group Filing (Check Applicable Line)
                                                                       
    / X / Form filed by One Reporting Person

    /   / Form filed by More than One Reporting Person     


                                  Page 1 of 3
                                SEC 1474 (7-96)


==================================================================================================================================== TABLE I - Non-Derivative Securities Acquired, Disposed of, or Beneficially Owned ==================================================================================================================================== 1. Title of Security 2. Trans- 3. Trans- 4. Securities Acquired (A) 5. Amount of 6. Ownership 7. Nature of (Instr. 3) action action or Disposed of (D) Securities Form: Indirect Date Code (Instr. 3, 4 and 5) Benefici- Direct (D) Beneficial (Instr. 8) ally Owned or In- Ownership --------- ----------- -------------------------- at End of direct (I) (Instr. 4) (Month/ Code V Amount (A) or (D) Price Month (Instr. 4) Day/ (Instr. 3 Year) and 4) Common Stock 5/5/1998 P 500.00 A 25.8125 D ------------------------ -------- ----- ----- --------- -------- ------- ---------- ------------ --------- Common Stock 5/5/1998 P 1,000.00 A 25.75 D ------------------------ -------- ----- ----- --------- -------- ------- ---------- ------------ --------- Common Stock 5/6/1998 P 1,000.00 A 25.5625 D ------------------------ -------- ----- ----- --------- -------- ------- ---------- ------------ --------- Common Stock 5/6/1998 P 1,000.00 A 25.50 6,000.00 D ------------------------ -------- ----- ----- --------- -------- ------- ---------- ------------ --------- ==================================================================================================================================== ==================================================================================================================================== Reminder: Report on a separate line for each class of securities beneficially owned directly or indirectly. * If the form is filed by more than one reporting person, see Instruction 4(b)(v).
Page 2 of 3 SEC 1474 (7-96)
==================================================================================================================================== TABLE II - Derivative Securities Acquired, Disposed of, or Beneficially Owned (e.g., puts, calls, warrants, options, convertible securities) ==================================================================================================================================== 1. Title of 2. Conver- 3. Trans- 4. Trans- 5. Number of 6. Date 7. Title and Derivative sion or action action Derivative Exercisable Amount of Security Exercise Date Code Securities and Under- (Instr. 3) Price of (Month/ (Instr. 8) Acquired (A) Expiration lying Deriva- Day/ or Disposed Date Securities tive Year) of (D)(Instr. (Month/Day/ (Instr. 3 Security 3, 4 and 5) Year) and 4) Date Expir- Amount or Exer- ation Number of Code V (A) (D) cisable Date Title Shares --------------- --------- -------- ------ ----- ------- ------- -------- -------- ------- ---------- ==================================================================================================================================== Table II (continued) ==================================================================================================================================== 8. Price of 9. Number of 10. Ownership 11. Nature of Derivative Derivative Form of Indirect Security Securities Derivative Beneficial (Instr. 5) Benefic- Security: Ownership ially Direct (D) (Instr. 4) Owned at or Indirect End of Month (I)(Instr. 4) (Instr. 4) ------------ ------------- ------------- ------------ ==================================================================================================================================== ====================================================================================================================================
Explanation of Responses: ** Intentional misstatements or omissions of facts constitute Federal Criminal Violations. See 18 U.S.C. 1001 and 15 U.S.C. 78ff(a). Note: File three copies of this Form, one of which must be manually signed. If space is insufficient, see Instruction 6 for procedure. Potential persons who are to respond to the collection of information contained in this form are not required to respond unless the form displays a currently valid OMB Number. /s/ Miriam Rogers Singer ----------------------------------- **Signature of Reporting Person (on behalf of Douglas H. Hunt) June 9, 1998 ----------------- Date Page 3 of 3 SEC 1474 (7-96)6