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
Kimmel, Jeanette C.
300 East 56th Avenue, Apt. 29-F
New York, NY USA 10022
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
05/31/98
If Amendment, Date of Original (Month/Year)
Relationship of Reporting Person to Issuer (Check all applicable)
(x) Director ( ) 10% Owner ( ) Officer (give title below)
( ) Other (specify below)
<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 | | | | | | |125000 |D | |
| | | | | | | | | |
- -----------------------------------------------------------------------------------------------------------------------------------|
<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>
1994 Stk. Opt. Plan |12.875 | | | | | |05/17|05/10|Common Stock|1000 | |1000 |D | |
| | | | | | |/94 |/01 | | | | | | |
- -----------------------------------------------------------------------------------------------------------------------------------|
1994 Stk. Opt. Plan |11.625 | | | | | |05/16|05/15|Common Stock|1000 | |1000 |D | |
| | | | | | |/95 |/02 | | | | | | |
- -----------------------------------------------------------------------------------------------------------------------------------|
1994 Stk. Opt. Plan |12.000 | | | | | |05/21|05/20|Common Stock|1000 | |1000 |D | |
| | | | | | |/96 |/03 | | | | | | |
- -----------------------------------------------------------------------------------------------------------------------------------|
1994 Stk. Opt. Plan |7.750 | | | | | |05/20|05/19|Common Stock|1000 | |1000 |D | |
| | | | | | |/97 |/04 | | | | | | |
- -----------------------------------------------------------------------------------------------------------------------------------|
1994 Stk. Opt. Plan |9.4375 |05/19|A |V|1000 | |05/19|05/18|Common Stock|1000 | |1000 |D | |
| |/98 | | | | |/98 |/05 | | | | | | |
- -----------------------------------------------------------------------------------------------------------------------------------|
___________________________________________________________________________________________________________________________________|
</TABLE>
JEANETTE C. KIMMEL
SIGNATURE OR REPORTING PERSON
JEANETTE C. KIMMEL
DATE
06/17/98
