This paper uses a two-country, two-good, conjectural-variations model of trade to show that a quota war will not end in autarky as Rodriguez (1974) and Tower (1975) concluded. Since both countries expect retaliatory responses to reductions in their quotas, both countries are willing to stop the trade war before autarky is reached. The possible equilibria are free trade, two equilibria in which one country has its optimal quota while the other country chooses free trade, and an interior solution. It is possible that some, all, or none of these equilibria will exist. Copyright 1995 by Blackwell Publishing Ltd.