There are two figures in Greek mythology known as Euphemus (Greek: Εὔφημος) "reputable".
One was the son of Poseidon, granted by his father the power to walk on water. Euphemus's mother is variously named: Europe, daughter of the giant Tityos; Oris, daughter of Orion; or Macionice, daughter of Eurotas. His residence is given as Panopeus in Phocis, or Hyria in Boeotia, or Taenarum in Laconia. Euphemus joined the voyage of the Argonauts, and served the crew well as helmsman. By a Lemnian woman (Malicha, Malache, or Lamache) he became the father of Leucophanes. Medea prophesied that he would one day rule Libya; her prophesy came true when Battus of Thera, an alleged distant descendant of Euphemus (by 17 generations), founded Cyrene.
The other Euphemus, son of Troezenus, was a leader of the Thracian Cicones, on the side of the Trojans, mentioned in Book II of the Iliad.
Euphemus is also a character in the work by Thucydides in the Peloponnisian War.
（Εὔφημος). 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.