A generalized parallel pore and surface diffusion model and associated dynamic simulation program have been developed for multicomponent fixed-bed ion-exchange processes. Both equilibrium and nonequilibrium mass action laws are used to describe stoichiometric ion exchange. Model equations are solved numerically for frontal, pulse, or sequential loading processes. Analytical solutions obtained from a local equilibrium theory for binary systems and experimental data of two multicomponent systems served as benchmarks for the numerical solutions. The results indicate that the parallel pore and surface diffusion model should be considered for nonlinear large-particle systems. A parametric study shows that a major difference in fixed-bed dynamics between mass action and Langmuir systems lies in the propagation of diffuse waves of multivalent ions. Generally, the higher the valence or mass action equilibrium constant, the more pronounced the tailing of diffuse waves, which results in apparent adsorption hysteresis in a loading and washing cycle. The apparently irreversibly adsorbed multivalent ions can be eluted by concentrated solutions of lower valence ions, as a result of the relative selectivities of the higher valence against lower valence ions decreasing with increasing total solution phase concentration. This can lead to changes from favorable to unfavorable isotherms and self-sharpening waves to diffuse waves, or vice versa. Other results show that elution order can be reversed for heterovalent ions in elution and displacement chromatography.