Ajax:
Ajax was the son of Telamon, king of Salamis. After Achilles, he was the mightiest of the Greek heroes in the Trojan War. Ajax was a huge man, head and shoulders larger than the other Greeks, enormously strong but somewhat slow of speech. In the Iliad, he is often called the "wall" or "bulwark" (herkos) of the Greeks. When Achilles had withdrawn from the fighting at Troy, it was Ajax who went forth to meet Hector in single combat; by the time darkness fell the fight was still a stalemate, but Ajax had wounded Hector without sustaining injury himself
After Achilles' death, Ajax competed with Odysseus for the ownership of Achilles' armor. Both men delivered speeches explaining their own merits, but Odysseus was by far the more eloquent and won the prize. Ajax was driven mad by his disappointment. According to one account, he vowed vengeance on the Greeks and began slaughtering cattle, mistaking them for his former comrades-in-arms. He finally committed suicide.
Ajax is often called "Telemonian Ajax" or "the greater Ajax," to distinguish him from Ajax the Lesser the son of Oileus, who also fought for the Greeks at Troy.
Nestor:
The son of Neleus, King of Pylos, and Chloris. He was the only one who was spared when Heracles slew his father and his brothers. Nestor helped fight the centaurs, participated in the hunt for the Calydonian boar and was one of the Argonauts. When he was already of advanced age, he still participated in the expedition against Troy, where he, as oldest of the Greek heroes, excelled in wisdom, eloquence, and bravery.