Fifth century Greeks distinguished between hegemonia (legitimated leadership) and arkhe (control). Thucydides employed this distinction to track the changing nature of the Athenian Empire during the Peloponnesian War, and the ways in which a diminishing concern for balancing self-interest against justice corroded Athenian authority, made survival of the empire increasingly problematic and encouraged the disastrous expedition to Sicily. The Melian Dialogue—often cited by realists to justify a power-based approach to foreign policy—is intended to symbolize this decay. Building on our analysis of Thucydides, we examine the British, Soviet and American experiences with hegemony. A striking feature of the contemporary American situation is the extent to which American leaders claim hegemonia but deny any interest in arkhe. Rightly or wrongly, much of the rest of the world has the reverse perception. This seeming contradiction has important implications for US foreign policy and world politics more generally.