There are two figures in Greek mythology known as Euphemus (Εὔφημος).

a son of Poseidon and Europa, daughter of Tityus, husband of Laonomé, the sister of Heracles. His father conferred on him the gift of moving so swiftly over the sea that his feet remained dry. He was originally one of the Minyae of Panopeus in Phocis, but afterwards settled on the promontory of Taenarum in Laconia, and took part in the Calydonian hunt and the expedition of the Argonauts. When the Argonauts came to the lake of Triton, Triton gave Eumolpus a clod of earth, and Medea prophesied that if he threw this into the entrance of the lower world at Taenarum, his descendants of the tenth generation would be masters of Libya. The clod, however, was lost in the island of Thera, and his descendants were compelled to hold possession of this island, from which at length, in the seventeenth generation, Battus came forth and founded Cyrené in Libya. See Apollon. Rhod. ii. 562; Hygin. Fab.14; Herod.iv. 150.

The other was a leader of the Thracian Cicones, on the side of the Trojans, mentioned in Book II of the Iliad.:

Euphemus, son of god-nurtured Troezenus, 
son of Ceos, led Ciconian spearmen.

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