The a priori determination of all heteroazeotropes present in a multicomponent system isna necessary task when analyzing and designing heterogeneous distillation processes. Although there are currently several approaches for determining homogenous azeotropes, no systematic approach exists for the determination of heteroazeotropes. This paper addresses this deficiency by describing an approach for computing heteroazeotropes. Our work is an extension of the approach developed by Fidkowski et al. for computing homogeneous azeotropes. The algorithm consists of three phases: 1) obtaining homogeneous azeotropes and spurious homogeneous azeotropes corresponding to actual heteroazeotropes using a homogeneous homotopy map, 2) retrace branches corresponding to actual spurious homogeneous azeotropes and search for points of intersection of the homogeneous curves and a projection of the heterogeneous curves, defined by a heterogeneous homotopy map, using a root exclusion test, and 3) at these points of intersection, track the heterogeneous curves using a heterogeneous map to the heteroazeotropes. This approach is independent of the particular model of phase equilibrium and can be readily extended to systems containing more than two liquid phases in equilibrium.