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 * COURTOT PHILIPPE F   2. Issuer Name and Ticker or Trading Symbol QUALYS, INC. [QLYS] 5. Relationship of Reporting Person(s) to Issuer (Check all applicable) __X__ Director __X__ 10% Owner __X__ Officer (give title below) _____ Other (specify below) Chairman, President & CEO (Last) (First) (Middle) C/O QUALYS, INC., 919 E. HILLSDALE BLVD. 3. Date of Earliest Transaction (Month/Day/Year) 12/21/2018 (Street) FOSTER CITY, CA 94404 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 Stock 12/21/2018   A   56,250 (1) A $ 0 5,484,192 D   Common Stock 12/21/2018   A   33,089 (2) A $ 0 5,517,281 D   Common Stock 12/21/2018   A   33,088 (3) A $ 0 5,550,369 D   Common Stock               100,000 I See Footnote (4)

Reminder: Report on a separate line for each class of securities beneficially owned directly or indirectly.
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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

Reporting Owners

Reporting Owner Name / Address	Relationships
	Director	10% Owner	Officer	Other
COURTOT PHILIPPE F C/O QUALYS, INC. 919 E. HILLSDALE BLVD. FOSTER CITY, CA 94404	X	X	Chairman, President & CEO

Signatures

/s/ Bruce Posey by power of attorney for Philippe F. Courtot		12/27/2018
**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)	Each Restricted Stock Unit ("RSU") represents a contingent right to receive one share of the Issuer's Common Stock. One-sixteenth of the RSUs will commence vesting on January 1, 2019 and will vest at end of each quarter, subject to the Reporting Person continuing as a service provider through each such date.
(2)	Each performance-based Restricted Stock Unit ("PRSU") represents a contingent right to receive one share of the Issuer's Common Stock and will vest based on the achievement of goals that are not market price goals but based on operating performance goals for the period January 2019 through December 2021 subject to the Reporting Person continuing as a service provider through the date that performance is certified.
(3)	Each performance-based Restricted Share Unit ("PRSU") represents a contingent right to receive one share of the Issuer's Common Stock and will vest in 3 increments based on the achievement of goals that are not market price goals but based on operating performance goals for each of fiscal 2019, 2020, and 2021 subject to the Reporting Person continuing as a service provider through the date that performance is certified for the relevant fiscal year.
(4)	These shares are held directly by a custodian under the Uniform Gifts to Minors Act for the benefit of the Reporting Person's minor child.

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