Ajax, the name of two Greek chiefs in the Trojan war, distinguished as the greater and the lesser. The greater was the son of Tela-mon, king of Salamis, and third in direct male descent from Jupiter. He was second only to Achilles in martial prowess, equal to him in strength, but inferior in agility. He led the forces of the Salaminians, in 12 ships. Hector retired before the Telamonian Ajax on more than one occasion in the course of the war. At the death of Achilles, the arms of that hero were allotted to him who had deserved best of the Greeks. But two advanced claims to this honor, the greater Ajax and Ulysses. The former alleged his preeminence as a warrior, the latter as a counsellor. The arms were adjudged to Ulysses. Ajax went mad, committed many excesses, and slew himself. This catastrophe, which is only alluded to by Homer, forms the subject of the tragedy of Sophocles called the "Ajax." In the Odyssey, Ulysses is represented as descending to the infernal regions and there making fraternal overtures to Ajax, who stalks away without reply. He was worshipped in Salamis as its tutelary hero. - The lesser, son of Oileus, king of the Locrians, whom he led in 40 ships, was remarkable for his swiftness of foot.

Having excited the anger of the gods, they raised a storm against his fleet as he was returning home. The Oi'le-an escaped to a rock, and defied the vengeance of the gods, whereupon Neptune cleft the rock with his trident, and threw Ajax into the sea. His fate is, however, variously told by the poets. According to some, his crime was the violation of Cassandra in the temple of Minerva, at the sack of Troy.