1. A son of Poseidon by Europe, the daughter of Tityus, or by Mecionice or Oris, a daughter of Orion or Eurotas. (Schol. ad Pind. Pyth. iv. 15; Tzetz. Chil. ii. 43.) According to the one account he was an inhabitant of Panopeus on the Cephissus in Phocis, and according to the other of Hyria in Boeotia, and afterwards lived at Taenarus. By a Lemnian woman, Malicha, Malache, or Lamache, he became the father of Leucophanes (Schol. ad Pind. Pyth. iv. 455; Tzetz. ad Lycoph. 886); but he was married to Laonome, the sister of Heracles. Euphemus was one of the Calydonian hunters, and the helmsman of the vessel of the Argonauts, and, by a power which his father had granted to him, he could walk on the sea just as on firm ground. (Apollon. Rhod. i. 182.) He is mentioned also as the ancestor of Battus, the founder of Cyrene, and the following story at once connects him with that colony. When the Argonauts carried their ship through Libya to the coast of the Mediterranean, Triton, who would not let them pass without showing them some act of friendship, offered them a clod of Libyan earth. None of the Argonauts would accept it; but Euphemus did, and with the clod of earth he received for his descendants the right to rule over Libya. Euphemus was to throw the piece of earth into one of the chasms of Taenaron in Peloponnesus, and his descendants, in the fourth generation, were to go to Libya and take it into cultivation. When, however, the Argonauts passed the island of Calliste, or Thera, that clod of earth by accident fell into the sea, and was carried by the waves to the coast of the island. The colonization of Libya was now to proceed from Thera, and although still by the descendants of Euphemus, yet not till the seventeenth generation after the Argonauts. The seventeenth descendant of Euphemus was Battus of Thera. (Pind. Pyth. iv. 1, &c.; Apollon. Rhod. ii. 562; Hygin. Fab. 14, 173; Herod. iv. 150.) According to Apollonius Rhodius (iv. 1755), the island of Thera itself had arisen from the clod of earth, which Euphemus purposely threw into the sea. Euphemus was represented on the chest of Cypselus as victor, with a chariot and two horses. (Paus. v. 17. § 4.)

2. A descendant of the river Axius who was the father of Eurybarus. (Anton. Lib. 8.)

3. There is also another mythical personage of this name. (Hom. Il. ii. 846.)