The technique proposed here for the evaluation of azeotrope lines by molecular simulation builds on ideas used to devise the Gibbs-Duhem integration (GDI) technique for evaluating phase equilibria by molecular simulation. Beginning with a known azeotropic state point, the method integrates a differential equation for the locus of azeotropes with a single semigrand-ensemble molecular simulation performed at each integration state point. Unlike the standard GDI method, fluctuation quantities are needed to conduct the integration. Although these quantifies are measured less precisely than simple ensemble averages, the integration is not adversely affected by this difficulty The method is demonstrated by applying to three model Lennard-Jones binaries. Among these mixtures is one in which the molecular diameter of one species is varied along the azeotrope line. This application shows how details of the intermolecular interactions affect azeotropic behavior: Such an understanding might be useful in formulating additives to break an azeotrope.