(Τέκμησσα), the daughter of the Phrygian king Teleutas, whose territory was ravaged by the Greeks during a predatory excursion from Troy. Teemessa was made prisoner, and was given to Ajax, the son of Telamon, who lived with her as his wife, and had by her a son, Eurysaces. (Soph. Ajax ; Schol. ad Hom. Il. 1.138.)