This paper proves the existence and uniqueness of Cournot equilibrium in models of international trade under oligopoly. The existence of Cournot equilibrium is established without the usual assumption that profit functions are concave. Instead the proof uses a weaker "aggregate concavity" condition. A simple proof is used to establish the uniqueness of the equilibrium. And, the paper considers the implications of the assumptions, used to prove the existence and uniqueness of the equilibrium, on the comparative static results.