The traditional literature derives optimum and revenue-maximizing export taxes within two-country models. with one exporter and one importer (Johnson 1950-51, Tower 1977). In reality, most products, including primary products. are exported by several countries. In this paper, we present a theory of trade taxes in a three-country framework. This enables us to deal with strategic interactions among exporting countries. We show that (i) if one of the countries is a Stackelberg leader, both countries improve their welfare relative to Nash equilibrium, and in the symmetric case, the follower's welfare is higher than that of the leader; (ii) the revenue-maximizing Nash tax is larger than the optimum tax for each country; and (iii) welfare may be higher in the revenue-maximizing Nash equilibrium than in the welfare-maximizing Nash equilibrium, a result which cannot arise in two-country models.