Pausanias relates that after Euippus, son of king Megareus, was killed by the Lion of Cithaeron, Megareus, whose elder son Timalcus had likewise fallen by the hands of Theseus, offered his daughter Euaechme and his kingdom to anyone who could slay the lion. Alcathous undertook the task, killed the lion, and thus obtained Euaechme for his wife, and afterwards became the successor of Megareus. In gratitude for this success, he built at Megara a temple of ArtemisAgrotera and ApolloAgraeus. He also restored the walls of Megara, which had been destroyed by the Cretans. In this work he was said to have been assisted by Apollo, and the stone upon which the god used to place his lyre while he was at work, was even in late times believed to produce a sound similar to that of a lyre when struck.
Echepolis, one of the sons of Alcathous, was killed during the Calydonian hunt in Aetolia, and when his brother Callipolis hastened to carry the sad tidings to his father, he found him engaged in offering a sacrifice to Apollo, and thinking it unfit to offer sacrifices at such a moment, he snatched away the wood from the altar. Alcathous imagining this to be an act of deliberate sacrilege, killed his son on the spot with a piece of wood. The acropolis of Megara was called by a name derived from that of Alcathous.
Alcathous was grandfather of the hero Ajax, via his daughter Periboea, who married Telamon, and of Iolaus, nephew and charioteer of Heracles, by his other daughter Automedusa.