As the Iliad comes to a close, Ajax and the majority of other Greek warriors are alive and well.When Achilles dies, killed by Paris (with help from Apollo), Ajax and Odysseus are the heroes who fight against the Trojans to get the body and bury it with his companion, Patroclus.When Patroclus is killed, Hector tries to steal his body.Ajax, assisted by Menelaus, succeeds in fighting off the Trojans and taking the body back with his chariot; however, the Trojans have already stripped Patroclus of Achilles' armor.In the Iliad, Ajax is notable for his abundant strength and courage, seen particularly in two fights with Hector.In Book 7, Ajax is chosen by lot to meet Hector in a duel which lasts most of a whole day.Most notably, Ajax is not wounded in any of the battles described in the Iliad, and he is the only principal character on either side who does not receive substantial assistance from any of the gods (except for Agamemnon) who take part in the battles, although, in book 13, Poseidon strikes Ajax with his staff, renewing his strength.Unlike Diomedes, Agamemnon, and Achilles, Ajax appears as a mainly defensive warrior, instrumental in the defence of the Greek camp and ships and that of Patroclus' body.
In Book 15, Hector is restored to his strength by Apollo and returns to attack the ships.
Ajax is responsible for the death of many Trojans lords, including Phorcys.
Ajax often fought in tandem with his brother Teucer, known for his skill with the bow.
Ajax at first gets the better of the encounter, wounding Hector with his spear and knocking him down with a large stone, but Hector fights on until the heralds, acting at the direction of Zeus, call a draw, with the two combatants exchanging gifts, Ajax giving Hector a purple sash and Hector giving Ajax his sharp sword.
The second fight between Ajax and Hector occurs when the latter breaks into the Mycenaean camp, and fights with the Greeks among the ships.