The welfare dominance of ad valorem taxes over unit taxes in a single-market Cournot oligopoly is well known. This article extends the analysis to multimarket oligopoly. Provided all ad valorem taxes are equal and positive, unit costs are constant, firms are active in all considered markets, and a representative consumer has convex preferences, ad valorem taxes are shown to dominate in multiproduct equilibrium. Conditions exist, however, under which economic efficiency declines upon replacing specific taxes with ad valorem taxes that preserve output levels. We discuss the roles of unit cost covariances across multiproduct firms, and also of complementarity in demand, in determining the extent of cost efficiencies arising under ad valorem taxation. For goods that are complementary or independent in demand, conditions are found such that industry profits decline upon use of ad valorem taxes.