CONE MILLS CORP
SC 13G/A, 1998-06-08
BROADWOVEN FABRIC MILLS, COTTON
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UNITED STATES
SECURITIES AND EXCHANGE COMMISSION
Washington, D.C.  20549

SCHEDULE 13G

Under the Securities Exchange Act of 1934
(Amendment No. 2)

Cone Mills Corporation
(Name of Issuer)

Common Stock
(Title of Class of Securities)

206814 10 5
(CUSIP Number)



Check the appropriate box to designate the rule pursuant to which this 
Schedule is filed:

     [X] Rule 13d-1(b)
     [ ] Rule 13d-1(c)
     [ ] Rule 13d-1(d)

*The remainder of this cover page shall be filled out for a reporting 
person's initial filing on this form with respect to the subject class 
of securities, and for any subsequent amendment containing information 
which would alter the disclosures provided in a prior cover page.

The information required in the remainder of this cover page shall not 
be deemed to be "filed" for the purpose of Section 18 of the Securities 
Exchange Act of 1934 ("Act") or otherwise subject to the liabilities of 
that section of the Act but shall be subject to all other provisions of 
the Act (however, see the Notes).



                                   13G

CUSIP NO.  206814 10 5


1)        NAME OF REPORTING PERSON
          S.S. OR I.R.S. IDENTIFICATION NO. OF ABOVE PERSON

            Norwest Corporation
            Tax Identification No.  41-0449260

2)        CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP*    (a)  [ ]
                                                               (b)  [ ]
3)        SEC USE ONLY

4)        CITIZENSHIP OR PLACE OF ORGANIZATION

            Delaware

NUMBER OF          (5)  SOLE VOTING POWER
SHARES                    1,153,900
BENEFICIALLY       (6)  SHARED VOTING POWER
OWNED BY                  500
EACH               (7)  SOLE DISPOSITIVE POWER
REPORTING                 1,149,00
PERSON             (8)  SHARED DISPOSITIVE POWER
WITH                      4,900

9)         AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON
             1,159,800

10)        CHECK IF THE AGGREGATE AMOUNT IN ROW (9) EXCLUDES CERTAIN 
           SHARES*

11)        PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW (9)
             Less than 5%

12)        TYPE OF REPORTING PERSON*

             HC

                                   13G

CUSIP NO.  206814 10 5


1)        NAME OF REPORTING PERSON
          S.S. OR I.R.S. IDENTIFICATION NO. OF ABOVE PERSON

            Norwest Bank Colorado, National Association
            Tax Identification No.  84-0187632

2)        CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP*    (a)  [ ]
                                                               (b)  [ ]
3)        SEC USE ONLY

4)        CITIZENSHIP OR PLACE OF ORGANIZATION

            United States of America

NUMBER OF          (5)  SOLE VOTING POWER
SHARES                    1,143,400
BENEFICIALLY       (6)  SHARED VOTING POWER
OWNED BY                  500
EACH               (7)  SOLE DISPOSITIVE POWER
REPORTING                 1,138,500
PERSON             (8)  SHARED DISPOSITIVE POWER
WITH                      4,900

9)         AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON
             1,143,900

10)        CHECK IF THE AGGREGATE AMOUNT IN ROW (9) EXCLUDES CERTAIN 
           SHARES*

11)        PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW (9)
             Less than 5%

12)        TYPE OF REPORTING PERSON*

             BK

SECURITIES AND EXCHANGE COMMISSION
Washington, D.C.  20549

SCHEDULE 13G
Under the Securities Exchange Act of 1934
(Amendment No. 2)


DISCLAIMER:  Information in this Schedule 13G is provided solely for 
the purpose of complying with Sections 13(d) and 13(g) of the Act and 
regulations promulgated thereunder, and is not to be construed as an 
admission that Norwest Corporation or any of its subsidiaries is the 
beneficial owner of the securities covered by this Schedule 13G for any 
purpose whatsoever.

Item 1(a)  Name of Issuer:

           Cone Mills Corporation

Item 1(b)  Address of Issuer's Principal Executive Offices:

           3101 North Elm Street
           Greensboro, NC  27408

Item 2(a)  Name of Person Filing:

           1.  Norwest Corporation
           2.  Norwest Bank Colorado, Inc.  (NBC)

Item 2(b)  Address of Principal Business Office:

           1.  Norwest Corporation
               Norwest Center
               Sixth and Marquette
               Minneapolis, MN  55479-1026

           2.  Norwest Bank Colorado, National Association
               1740 Broadway
               Denver, CO  80274-8677

Item 2(c)  Citizenship:

           1.  Norwest Corporation:  Delaware
           2.  NBC:  United States

Item 2(d)  Title of Class of Securities:

           Common Stock

Item 2(e)  CUSIP Number:

           206814 10 5


Item 3     The person filing is a:

           1.  Norwest Corporation:  Parent Holding Company in
               accordance with 240.13d-1(b)(1)(ii)(G)
           2.  NBC:  Bank as defined in Section 3(a)(6) of the Act

Item 4     Ownership:

           (a)  Amount beneficially owned:  1,159,800 shares (includes
                1,143,900 shares deemed to be beneficially owned by
                NBC)

           (b)  Percent of class:  Less than 5%

           (c)  Number of shares as to which such person has:

               (i)    Sole power to vote or direct the vote:  1,153,900

               (ii)   Shared power to vote or direct the vote:  500

               (iii)  Sole power to dispose or to direct the
                      disposition of:  1,149,000

               (iv)   Shared power to dispose or direct the disposition 
                      of:  4,900

Item 5     If this statement is being filed to report the fact that as
           of the date hereof the reporting persons have ceased to be
           beneficial owners of more than five percent of the class of
           securities, check the following [X].

Item 6     Ownership of More than Five Percent on Behalf of Another 
           Person:

           Persons other than Norwest Corporation and its subsidiaries
           have the right to receive, or the power to direct the
           receipt of, dividends from, or the proceeds from the sale
           of, such securities.  To the knowledge of Norwest
           Corporation, no interest of any such person represents more
           than 5% of the class.

Item 7     Identification and Classification of the Subsidiary Which 
           Acquired the Security Being Reported on by the Parent
           Holding Company:

           See Attachment A.

Item 8     Identification and Classification of Members of the Group:

           Not Applicable.

Item 9     Notice of Dissolution of Group:

           Not Applicable.


Item 10    Certification:

           By signing below, I certify that, to the best of my
           knowledge and belief, the securities referred to above were
           acquired in the ordinary course of business and were not
           acquired for the purpose of and do not have the effect of
           changing or influencing the control of the issuer of such
           securities and were not acquired in connection with or as a
           participant in any transaction having such purposes or
           effect.

Signature.

After reasonable inquiry and to the best of my knowledge and belief, I 
certify that the information set forth in this statement is true, 
complete, and correct.

Date:  June 5, 1998

NORWEST CORPORATION



By:  /s/ Laurel A. Holschuh
         Laurel A. Holschuh, Senior Vice President
          and Secretary


ATTACHMENT A

The Schedule 13G to which this attachment is appended is filed on 
behalf of the subsidiaries listed below, all of which are classified 
for purposes of Regulation 13d-1(b)(1)(ii)(B) as banks.

Norwest Bank Colorado, National Association

Norwest Bank Minnesota, National Association







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