Bias married his cousin Pero who was the daughter of Neleus. It was said that Neleus would not allow his daughter to marry anyone unless the suitor brought him the oxen of Iphiclus. This Melampus achieved with courage and using his supernatural abilities of speaking with animals, upon winning the challenge he arranged the marriage of Pero and Bias, they had one child together, Talaus.
When Pero died Bias remarried Iphianassa, daughter of Proetus, after Melampus had cured her, her sisters and the Argive women from madness. He received one third of Proetus's kingdom all of which he gave to Bias. Bias and Iphianassa had a daughter Anaxibia who married Pelias, to whom she bore Acastus and several daughters. According to Pausanias, Amythaon is the father of Bias and Melampus. Their mother was Idomene, daughter of Pheres or Abas of Argos.
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