Euthydemos and Euthydemus are two English transcriptions of the same name in Greek. There are two characters of this name in Socratic literature. In Book I of The Memorabilia, Xenophon relates Critias' passion for the young Euthydemos and how Socrates mocked him for it: "Socrates had observed that Critias loved Euthydemos and wanted to have his way with him. Therefore Socrates tried to argue him out of it, saying that it was degrading for a free man and ill became someone "beautiful in body and mind" to importune, moreover for nothing good, his beloved to whom he should be a shining example. Critias, Athenian sophist and politician, was the leader of the "Thirty Tyrants" who after the Peloponnesian War ruled for a short while over Athens (404 BC).
Another Euthydemos is the eponymous character in one of Plato's Dialogues, Euthydemus. It is a fairly odd dialogue on logic and logical fallacies, or sophisms. The characters of Euthydemus and his brother are sophists questioned by Socrates in a confrontation of the Euthydemian Eristic and the Socratic Elenchos.