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

UNITED STATES SECURITIES AND EXCHANGE COMMISSION Washington, D.C. 20549 STATEMENT OF CHANGES IN BENEFICIAL OWNERSHIP OF SECURITIES 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(h) of the Investment Company Act of 1940

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(Print or Type Responses)

1. Name and Address of Reporting Person * HAWKINS WILLIAM H II   2. Issuer Name and Ticker or Trading Symbol CONVERGYS CORP [CVG] 5. Relationship of Reporting Person(s) to Issuer (Check all applicable) _____ Director _____ 10% Owner __X__ Officer (give title below) _____ Other (specify below) SVP General Counsel (Last) (First) (Middle) 201 EAST FOURTH STREET, PO BOX 1638 3. Date of Earliest Transaction (Month/Day/Year) 11/05/2004 (Street) CINCINNATI, OH 45201 4. If Amendment, Date Original Filed(Month/Day/Year) 6. Individual or Joint/Group Filing(Check Applicable Line) _X_ Form filed by One Reporting Person ___ Form filed by More than One Reporting Person (City) (State) (Zip) Table I - Non-Derivative Securities Acquired, Disposed of, or Beneficially Owned

1.Title of Security (Instr. 3) 2. Transaction Date (Month/Day/Year) 2A. Deemed Execution Date, if any (Month/Day/Year) 3. Transaction Code (Instr. 8) 4. Securities Acquired (A) or Disposed of (D) (Instr. 3, 4 and 5) 5. Amount of Securities Beneficially Owned Following Reported Transaction(s) (Instr. 3 and 4) 6. Ownership Form: Direct (D) or Indirect (I) (Instr. 4) 7. Nature of Indirect Beneficial Ownership (Instr. 4) Code V Amount (A) or (D) Price Common Shares               91,008 D   Common Shares               1,578.144 I By Trustee of RSP (1)

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Table II - Derivative Securities Acquired, Disposed of, or Beneficially Owned
(e.g., puts, calls, warrants, options, convertible securities)

1. Title of Derivative Security (Instr. 3)

2. Conversion or Exercise Price of Derivative Security

3. Transaction Date (Month/Day/Year)

3A. Deemed Execution Date, if any (Month/Day/Year)

4. Transaction Code (Instr. 8)

5. Number of Derivative Securities Acquired (A) or Disposed of (D) (Instr. 3, 4, and 5)

6. Date Exercisable and Expiration Date (Month/Day/Year)

7. Title and Amount of Underlying Securities (Instr. 3 and 4)

8. Price of Derivative Security (Instr. 5)

9. Number of Derivative Securities Beneficially Owned Following Reported Transaction(s) (Instr. 4)

10. Ownership Form of Derivative Security: Direct (D) or Indirect (I) (Instr. 4)

11. Nature of Indirect Beneficial Ownership (Instr. 4)

Code

V

(A)

(D)

Date Exercisable

Expiration Date

Title

Amount or Number of Shares

Option (2) (3)

$ 0

(4)

(4)

Common Shares

0

172,344

D

Phantom Share Unit (5)

$ 0 (6)

11/05/2004

11/05/2004

P

40.738

(5)

(5)

Common Shares

40.738

(5)

1,251.886

D

Reporting Owners

Reporting Owner Name / Address	Relationships
	Director	10% Owner	Officer	Other
HAWKINS WILLIAM H II 201 EAST FOURTH STREET PO BOX 1638 CINCINNATI, OH 45201			SVP General Counsel

Signatures

/s/ William H. Hawkins II		11/08/2004
**Signature of Reporting Person		Date

Explanation of Responses:

*	If the form is filed by more than one reporting person, see Instruction 4(b)(v).
**	Intentional misstatements or omissions of facts constitute Federal Criminal Violations. See 18 U.S.C. 1001 and 15 U.S.C. 78ff(a).
(1)	Common shares balance held in Retirement Savings Plan.
(2)	Option shares granted under the Convergys 1998 Long Term Incentive Plan, which is a Rule 16b-3 Plan.
(3)	Right to buy.
(4)	Option shares granted on various dates under the Convergys 1998 Long Term Incentive Plan, which is a Rule 16b-3 Plan.
(5)	Acquired on various dates between January 1 and November 5, 2004 pursuant to the Convergys Corporation Executive Deferred Compensation Plan, at prices ranging from $12.30 and $19.96 per share. Phantom shares are payable in cash or common shares of the Company upon termination of employment.
(6)	Security converts to common stock on a one-for-one basis.

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