In this article, we demonstrate the existence of various types of singularities in equilibrium and nonequilibrium reactive separation process problems. First, the equilibrium reactive separation process problem is posed as a set of differential algebraic equations (DAEs), and it is shown that Hopf bifurcation points can exist, even for this formulation, for both the methyl tert-butyl ether (MTBE) and tert-amyl methyl ether (TAME) systems. Extension of this analysis to nonequilibrium models shows the existence of limit points, in the case of the TAME mixture, and isolas with intersecting branches, in the case of the MTBE mixture.