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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1. Name and Address of Reporting Person * BERGERON SANDRA E.   2. Issuer Name and Ticker or Trading Symbol QUALYS, INC. [QLYS] 5. Relationship of Reporting Person(s) to Issuer (Check all applicable) __X__ Director _____ 10% Owner _____ Officer (give title below) _____ Other (specify below) (Last) (First) (Middle) C/O QUALYS, INC., 1600 BRIDGE PARKWAY 3. Date of Earliest Transaction (Month/Day/Year) 06/06/2016 (Street) REDWOOD CITY, CA 94065 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 06/06/2016   A   6,173 (1) A $ 0 28,673 D   Common Stock               50,000 I See Footnote (2) Common Stock               90,000 I See Footnote (3)

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
BERGERON SANDRA E. C/O QUALYS, INC. 1600 BRIDGE PARKWAY REDWOOD CITY, CA 94065	X

Signatures

/s/ Bruce Posey by power of attorney		06/07/2016
**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)	The reported securities represent restricted stock units which vest on the earlier of (i) June 6, 2017 or (ii) the day before the Issuer's 2017 annual meeting of stockholders, subject to the Reporting Person's continued service through each such vesting date.
(2)	Shares held directly by DBG Investments Inc., an investment company solely owned by the spouse of the Reporting Person. The Reporting Person disclaims beneficial ownership of these securities except to the extent of its pecuniary interest therein, and the inclusion of these securities in this report shall not be deemed an admission of beneficial ownership of the reported securities for purposes of Section 16 or any other purpose.
(3)	Shares held directly by the Bergeron Family Trust dtd 11/15/2004, for which the Reporting Person serves as trustee.

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