CONE MILLS CORP
4, 1998-08-05
BROADWOVEN FABRIC MILLS, COTTON
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U.S. SECURITIES AND EXCHANGE COMMISSION
WASHINGTON, D.C. 20549
FORM 4
STATEMENT OF CHANGES IN BENEFICIAL OWNERSHIP
[ ] Check box if no longer subject to Section 16.
Form 4 or Form 5 obligations may continue. See Instructions 1(b).
1. Name and Address of Reporting Person
   Woolen, Marvin A.
   3101 N. Elm St.
   Greensboro, NC USA 27415-6540
2. Issuer Name and Ticker or Trading Symbol
   CONE MILLS CORPORATION COE
3. IRS or Social Security Number of Reporting Person (Voluntary)
   
4. Statement for Month/Year
   07/31/98
If Amendment, Date of Original (Month/Year)
   
Relationship of Reporting Person to Issuer (Check all applicable)
   ( ) Director  ( ) 10% Owner (x) Officer (give title below)
   ( ) Other (specify below)
   Vice President
<TABLE>
<CAPTION>
___________________________________________________________________________________________________________________________________
 Table I -- Non-Derivative Securities Acquired, Disposed of, or Beneficially Owned                                                 |
___________________________________________________________________________________________________________________________________|
1. Title of Security       |2.    |3.    |4.Securities Acquired (A)         |5.Amount of        |6.Dir |7.Nature of Indirect       |
                           | Transaction |  or Disposed of (D)              |  Securities       |ect   |  Beneficial Ownership     |
                           |      |      |                                  |  Beneficially     |(D)or |                           |
                           |      |    | |                  | A/|           |  Owned at         |Indir |                           |
                           | Date |Code|V|    Amount        | D |    Price  |  End of Year      |ect(I)|                           |
___________________________________________________________________________________________________________________________________|
<S>                        <C>    <C>  <C><C>               <C> <C>         <C>                 <C>    <C>
Common Stock               |      |    | |                  |   |           |4000               |D     |                           |
- -----------------------------------------------------------------------------------------------------------------------------------|
Common Stock               |      |    | |                  |   |           |1975               |I     |by 401(k) Trust [1]        |
- -----------------------------------------------------------------------------------------------------------------------------------|
Common Stock               |      |    | |                  |   |           |500                |I     |by custody for son         |
- -----------------------------------------------------------------------------------------------------------------------------------|
Common Stock               |07/23/|P   | |5000              |A  |7.6875     |5000               |I     |by Mother [2]              |
                           |98    |    | |                  |   |           |                   |      |                           |
- -----------------------------------------------------------------------------------------------------------------------------------|
<CAPTION>
___________________________________________________________________________________________________________________________________
 Table II -- Derivative Securitites Acquired, Disposed of, or Beneficially Owned                                                   |
___________________________________________________________________________________________________________________________________|
1.Title of Derivative |2.Con-  |3.   |4.    |5.Number of De |6.Date Exer|7.Title and Amount  |8.Price|9.Number    |10.|11.Nature of|
  Security            |version |Transaction | rivative Secu |cisable and|  of Underlying     |of Deri|of Deriva   |Dir|Indirect    |
                      |or Exer |     |      | rities Acqui  |Expiration |  Securities        |vative |tive        |ect|Beneficial  |
                      |cise    |     |      | red(A) or Dis |Date(Month/|                    |Secu   |Securities  |(D)|Ownership   |
                      |Price of|     |      | posed of(D)   |Day/Year)  |                    |rity   |Benefi      |or |            |
                      |Deriva- |     |      |               |Date |Expir|                    |       |ficially    |Ind|            |
                      |tive    |     |      |           | A/|Exer-|ation|   Title and Number |       |Owned at    |ire|            |
                      |Secu-   |     |    | |           | D |cisa-|Date |   of Shares        |       |End of      |ct |            |
                      |rity    |Date |Code|V|  Amount   |   |ble  |     |                    |       |Year        |(I)|            |
___________________________________________________________________________________________________________________________________|
<S>                   <C>      <C>   <C>  <C><C>        <C> <C>   <C>   <C>          <C>     <C>     <C>          <C> <C>
Employee Stock Option |8.00    |     |    | |           |   |05/08|01/06|Common Stock|15000  |       |15000       |D  |            |
(right to buy)        |        |     |    | |           |   |/97  |/06  |            |       |       |            |   |            |
- -----------------------------------------------------------------------------------------------------------------------------------|
Employee Stock Option |8.50    |     |    | |           |   |05/11|01/09|Common Stock|8000   |       |8000        |D  |            |
(right to buy)        |        |     |    | |           |   |/98  |/07  |            |       |       |            |   |            |
- -----------------------------------------------------------------------------------------------------------------------------------|
</TABLE>
Explanation of Responses:
1. Shares held in Company stock fund in the 401(k) Program. Since the valuation
period in the last report, the reporting person's account acquired 405 shares of
Common Stock.
2. Shares acquired for mother pursuant to power of attorney held by reporting
person and held in account in which reporting person may have pecuniary
interest.

MARVIN A. WOOLEN
SIGNATURE OF REPORTING PERSON
/Signature/
MARVIN A. WOOLEN
DATE
08/04/98



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