Ajax is a son of Oileus, a king of Locris, and his wife Eriopis. In order that he is not confused with the Telamonian Ajax, he is referred to as the Oilean Ajax, Ajax of Locris, or simply 'Little' Ajax.
During the Trojan War, Ajax led forty ships from Locris. During the Iliad, he is often seen fighting along side the greater Ajax. During the funeral games for Patroclus, he participates in a running event, but trips and loses to Odysseus.
During the fall of Troy, Ajax rapes Cassandra in the temple of Athena. Odysseus wants him to be stoned for this crime, but he clings to the same altar Cassandra had before.
As told in the Odyssey, on the voyage home, Athena attempts to kill Ajax. She sends a storm, which wrecks his ship. Ajax, however, is able to swim to an island. Once safe on the shore, he boasts that not even the gods can kill him. At that moment, Poseidon destroys the island itself with his trident, and Ajax drowns.