A class of models is derived for studying the effects of chemical kinetics on residue curve maps for reactive distillation. Activity-based rate and phase equilibrium expressions provide an accurate and thermodynamically consistent description of composition changes in nonideal, reacting vapor-liquid mixtures. For certain strategies of operation, which dictate the rate of product removal, the model equations are nonautonomous, leading to unusual dynamic behavior. However, for a certain special product removal policy, the effects of kinetics can be described by a single parameter, the Damkohler number, which measures the rate of reaction relative to product removal. For small values of the Damkohler number, the nonreactive simple distillation residue curve map is recovered and the singular points are the pure components and azeotropes in the nonreactive mixture. A bifurcation analysis shows the deformation and, in some cases, the disappearance of these singular points as the Damkohler number is increased until the equilibrium reactive residue curve map is recovered at large values. This bifurcation analysis reveals the limitations of the equilibrium analysis. A model problem for the reactive distillation of methyl tert-butyl ether from isobutene and methanol is solved.