Son of Cteatus
Amphimachus was the son of Zeus (son of Actor) and Theronice, daughter of Dexamenus. He was one of the leaders of the Elean contingent at the Trojan War (the other was Thalpius, son of Eurytus) and was slain by Hector.
Son of Nomion
Amphimachus was the son of Nomion. He and his brother Nastes were captains of the Carian contingent on the side of the Trojans in the Trojan war. Either he or his brother were killed by Achilles; according to the commentary to the Iliad by Thomas D. Seymour, his brother Nastes was the one killed and of whom the armour and golden ornaments were subsequently stripped off.
Son of Electryon
King of Elis
Suitors of Penelope
Amphimachus was one of the suitors of Penelope from Dulichium. He was ultimately killed by Odysseus. Another suitor of Penelope named Amphimachus was from Ithaca. He too was ultimately killed by Odysseus.
- Homer. The Iliad, 13.169 - But the rest fought on, and a cry unquenchable arose. And Teucer, son of Telamon, was first to slay his man, even the spearman Imbrius, the son of Mentor, rich in horses. He dwelt in Pedaeum before the sons of the Achaeans came, and had to wife a daughter of Priam that was born out of wedlock, even Medesicaste; but when the curved ships of the Danaans came he returned to Ilios and was pre-eminent among the Trojans, and he dwelt in the house of Priam, who held him in like honour with his own children. Him did the son of Telamon smite beneath the ear with a thrust of his long spear, and again drew forth the spear; and he fell like an ash-tree that, on the summit of a mountain that is seen from afar on every side, is cut down by the bronze, and bringeth its tender leafage to the ground; even so fell he, and about him rang his armour dight with bronze. And Teucer rushed forth eager to strip from him his armour, but Hector, even as he rushed, cast at him with his bright spear. Howbeit Teucer, looking steadily at him, avoided the spear of bronze by a little, but Hector smote Amphimachus, son of Cteatus, the son of Actor, in the breast with his spear as he was coming into the battle; and he fell with a thud, and upon him his armour clanged. Then Hector rushed forth to tear from the head of great-hearted Amphimachus the helm that was fitted to his temples, but Aias lunged with his bright spear at Hector as he rushed, yet in no wise reached he his flesh, for he was all clad in dread bronze; but he smote the boss of his shield, and thrust him back with mighty strength, so that he gave ground backward from the two corpses, and the Achaeans drew them off. Amphimachus then did Stichius and goodly Menestheus, leaders of the Athenians, carry to the host of the Achaeans, and Imbrius the twain Aiantes bare away, their hearts fierce with furious valour. And as when two lions that have snatched away a goat from sharp-toothed hounds, bear it through the thick brush, holding it in their jaws high above the ground, even so the twain warrior Aiantes held Imbrius on high, and stripped him of his armour. And the head did the son of Oïleus cut from the tender neck, being wroth for the slaying of Amphimachus, and with a swing he sent it rolling through the throng like a ball; and it fell in the dust before the feet of Hector.
- Apollodorus. The Library, E.3.12 - Of the Argives, Diomedes, son of Tydeus, and his company: they brought eighty ships. Of the Mycenaeans, Agamemnon, son of Atreus and Aerope: a hundred ships. Of the Lacedaemonians, Menelaus, son of Atreus and Aerope: sixty ships. Of the Pylians, Nestor, son of Neleus and Chloris: forty ships. Of the Arcadians, Agapenor: seven ships. Of the Eleans, Amphimachus and his company: forty ships. Of the Dulichians, Meges, son of Phyleus: forty ships. Of the Cephallenians, Ulysses, son of Laertes and Anticlia: twelve ships. Of the Aetolians, Thoas, son of Andraemon and Gorge: he brought forty ships.
- Homer. The Iliad, 2.615 - And they that dwelt in Buprasium and goodly Elis, all that part thereof that Hyrmine and Myrsinus on the seaboard and the rock of Olen and Alesium enclose between them—these again had four leaders, and ten swift ships followed each one, and many Epeians embarked thereon. Of these some were led by Amphimachus and Thalpius, of the blood of Actor, sons, the one of Cteatus and the other of Eurytus; and of some was the son of Amarynceus captain, even mighty Diores; and of the fourth company godlike Polyxeinus was captain, son of king Agasthenes, Augeias' son.
- Homer. The Iliad, 2.866 - And Nastes again led the Carians, uncouth of speech, who held Miletus and the mountain of Phthires, dense with its leafage, and the streams of Maeander, and the steep crests of Mycale. These were led by captains twain, Amphimachus and Nastes—Nastes and Amphimachus, the glorious children of Nomion. And he came to the war all decked with gold, like a girl, fool that he was; but his gold in no wise availed to ward off woeful destruction; nay, he was slain in the river beneath the hands of the son of Aeacus, swift of foot; and Achilles, wise of heart, bare off the gold.
- Homer, "2.872", Iliad (in Greek); "2.872", (in English); Seymour, Thomas D. (1891), "Commentary: Note 872", at the Perseus Project.
- Apollodorus. The Library, 2.4.6 - When Electryon reigned over Mycenae, the sons of Pterelaus came with some Taphians and claimed the kingdom of Mestor, their maternal grandfather, and as Electryon paid no heed to the claim, they drove away his kine; and when the sons of Electryon stood on their defence, they challenged and slew each other. But of the sons of Electryon there survived Licymnius, who was still young; and of the sons of Pterelaus there survived Everes, who guarded the ships. Those of the Taphians who escaped sailed away, taking with them the cattle they had lifted, and entrusted them to Polyxenus, king of the Eleans; but Amphitryon ransomed them from Polyxenus and brought them to Mycenae. Wishing to avenge his sons' death, Electryon purposed to make war on the Teleboans, but first he committed the kingdom to Amphitryon along with his daughter Alcmena, binding him by oath to keep her a virgin until his return. However, as he was receiving the cows back, one of them charged, and Amphitryon threw at her the club which he had in his hands. But the club rebounded from the cow's horns and striking Electryon's head killed him. Hence Sthenelus laid hold of this pretext to banish Amphitryon from the whole of Argos, while he himself seized the throne of Mycenae and Tiryns; and he entrusted Midea to Atreus and Thyestes, the sons of Pelops, whom he had sent for.
- Pausanias, Description of Greece, 5. 3. 4 - 5: Polyxenus came back safe from Troy and begat a son, Amphimachus. This name I think Polyxenus gave his son because of his friendship with Amphimachus, the son of Cteatus, who died at Troy. Amphimachus begat Eleius...
- Apollodorus, Bibliotheca, Epitome of Book 4, 7. 26 - 33: And on arriving in his native land Ulysses found his substance wasted; for, believing that he was dead, suitors were wooing Penelope. From Dulichium came fifty-seven: Amphinomus, Thoas... Amphimachus... Ceraus. ...And from Ithaca itself the suitors were twelve, to wit:- Antinous, Pronous... Amphimachus... Ctesippus. ...Now Penelope delivered to the suitors the bow of Ulysses, which he had once received from Iphitus; and she said that she would marry him who bent the bow. When none of them could bend it, Ulysses took it and shot down the suitors, with the help of Eumaeus, Philoetius, and Telemachus.
- Quintus Smyrnaeus. The Fall of Troy, 12.337 - Into that cavernous Horse Achilles' son first entered, strong Menelaus followed then, Odysseus, Sthenelus, godlike Diomede, Philoctetes and Menestheus, Anticlus, Thoas and Polypoetes golden-haired, Aias, Eurypylus, godlike Thrasymede, Idomeneus, Meriones, far-famous twain, Podaleirius of spears, Eurymachus, Teucer the godlike, fierce Ialmenus, Thalpius, Antimachus, Leonteus staunch, Eumelus, and Euryalus fair as a God, Amphimachus, Demophoon, Agapenor, Akamas, Meges stalwart Phyleus' son -- yea, more, even all their chiefest, entered in, so many as that carven Horse could hold. Godlike Epeius last of all passed in, the fashioner of the Horse; in his breast lay the secret of the opening of its doors and of their closing: therefore last of all he entered, and he drew the ladders up whereby they clomb: then made he all secure, and set himself beside the bolt. So all in silence sat 'twixt victory and death.