In this paper, we extend the streamtube approach described in Part I to compositional displacements. One-dimensional compositional solutions to three- and four-component problems are mapped along periodically updated streamtubes to yield two-dimensional compositional solutions for heterogeneous systems. In our technique, the complex physics describing multiphase, compositional flow is completely decoupled from the underlying grid used to describe reservoir heterogeneity, allowing the construction of approximate solutions using three to five orders of magnitude less computation time than traditional finite-difference/finite-element approaches. In addition, by mapping one-dimensional, diffusion-free solutions along streamtubes, the impact of numerical diffusion on displacement performance in standard numerical approaches can be estimated. We show, by example, that numerical diffusion may mitigate substantially, or even completely eliminate, any mobility contrast in a two-dimensional finite-difference compositional solution, resulting in optimistic recoveries.