
11 S.W.3d 342 (1999)
HARRIS COUNTY, Texas and Lillie Gibson, Appellants,
v.
Gregg Franklin CARR, Appellee.
No. 01-99-00654-CV.
Court of Appeals of Texas, Houston (1st Dist.).
December 23, 1999.
Rehearing Overruled February 18, 2000.
*343 Leslie Ruthe Johnson, Asst. County Atty.-Harris County, Michael P. Fleming, County Atty., Houston, for Appellant.
Joseph A. Scamardi, Sally Takacs Miller, Houston, for Appellee.
Panel consists of Justices MIRABAL, NUCHIA, and DUGGAN.[*]

OPINION
MARGARET GARNER MIRABAL, Justice.
Is Harris County, a self-insurer for workers' compensation purposes, exempt from the statute of limitations governing the time for filing a subrogation lawsuit? We conclude the County is not exempt, and accordingly we affirm the summary judgment in this case.

Case Background
The facts are undisputed. On February 11, 1994, Lillie Gibson's vehicle collided with a vehicle driven by Gregg Franklin Carr. Harris County, Gibson's employer, paid workers' compensation benefits to Gibson for injuries arising from the accident.
On October 21, 1997, Harris County, both on its own behalf and on Gibson's behalf as co-plaintiff, filed suit against Carr, claiming that Carr's alleged negligence caused Gibson's injuries. Carr filed a motion for summary judgment against both Harris County and Gibson, asserting the affirmative defenses of limitations bar and laches. In their response, Harris County and Gibson asserted that the statute of limitations and laches do not apply to them. The trial court granted summary judgment in favor of Carr without specifying the ground relied on.

Standard of Review
Summary judgment under Rule 166a(c) is proper only when the movant establishes there is no genuine issue of material fact, and that the movant is entitled to judgment as a matter of law. TEX.R. CIV. P. 166a(c); Randall's Food Mkts., Inc. v. Johnson, 891 S.W.2d 640, 644 (Tex.1995); Long v. State Farm Fire & Cas. Co., 828 S.W.2d 125, 126-27 (Tex. App.-Houston [1st Dist.] 1992, writ denied). A movant may obtain summary judgment by conclusively establishing all elements of an affirmative defense, such as limitations, as a matter of law. Science Spectrum, Inc. v. Martinez, 941 S.W.2d 910, 911 (Tex.1997); Jones v. Legal Copy, Inc., 846 S.W.2d 922, 924 (Tex.App.-Houston [1st Dist.] 1993, no writ). The summary judgment is affirmable on appeal if any ground asserted in the motion for summary judgment is a valid ground for rendering summary judgment. Cincinnati Life Ins. Co. v. Cates, 927 S.W.2d 623, 626 (Tex.1996).

Statute of Limitations
The two-year statute of limitations[1] applies to subrogation actions under the Texas Workers' Compensation Act.[2]*344 Guillot v. Hix, 838 S.W.2d 230, 233 (Tex. 1992). A subrogation claim, as well as the employee's third-party claim, accrue at the time of the employee's injury. Id. at 234-35. Thus, unless an exemption applies, the deadline for filing suit in this case was February 11, 1996. Suit was filed more than one and one-half years later, on October 21, 1997.
Harris County asserts it is exempt from the two-year limitations period pursuant to the general limitations exemption granted to various governmental entities under section 16.061 of the Civil Practices and Remedies Code. Gibson argues that if Harris County's claim is not barred, neither is her claim.
Section 16.061(a) provides:
A right of action of this state or a political subdivision of the state, including a county ... is not barred by any of the following sections [of the TEX. CIV. PRAC. & REM.CODE]: 16.001-16.004[3]....
TEX. CIV. PRAC. & REM.CODE ANN. § 16.061(a) (Vernon Supp.2000). By section 16.061, and its predecessors, the legislature has exempted counties and other entities, unlike ordinary litigants, from the limitations defense in appropriate cases. See Monsanto Co. v. Cornerstones Mun. Util. Dist., 865 S.W.2d 937, 938-40 (Tex.1993) (discussing the statutory amendment history of section 16.061). It is Carr's position that this is not an appropriate case for the application of section 16.061 because of the very nature of a workers' compensation subrogation claim. We agree with Carr.
The Texas Supreme Court has made it clear that a workers' compensation insurer who asserts a subrogation claim asserts a claim that belongs to the employee. Franks v. Sematech, Inc., 936 S.W.2d 959, 960 (Tex.1997). There is but one cause of action against the third-party tortfeasor, and it belongs to the employee. Id.; Guillot, 838 S.W.2d at 232. This is true irrespective of whether the insurer sues in its own name or the employee's name. Sematech, 936 S.W.2d at 960. Thus, the third-party tortfeasor in a workers' compensation subrogation action may assert defenses he would have had in a suit brought directly by the employee, such as a limitations defense. Guillot, 838 S.W.2d at 232-33.[4]
We hold that, because the subrogation claim brought by Harris County against Carr in the present case is a claim that belongs to Gibson, it is not a cause of action belonging to a political subdivision that is covered by the limitations exemption of Section 16.061 of the Civil Practices and Remedies Code. Accordingly, because Harris County, on behalf of itself and Gibson, filed suit against Carr more than three and one-half years after the subject car accident, the claim was barred by the two-year statute of limitations. Summary judgment on this basis was properly granted.
We overrule issues one, two, and three. It is not necessary to reach the merits of issue four dealing with the alternative ground for summary judgment, and we decline to do so.
We affirm the judgment.
NOTES
[*]  The Honorable Lee Duggan, Jr., retired Justice, Court of Appeals, First District of Texas at Houston, participating by assignment.
[1]  TEX. CIV. PRAC. & REM.CODE ANN. § 16.003 (Vernon Supp.2000)
[2]  TEX. LAB.CODE ANN. § 417.001 (Vernon Supp. 2000).
[3]  As previously noted, section 16.003 is the two-year statute of limitations applicable to this case.
[4]  We note that the Tillman case relied on by appellants was not a statutory subrogation case governed by the Workers' Compensation Act, and therefore it has no application to the present case. See City of Port Arthur v. Tillman, 398 S.W.2d 750 (Tex.1965).
