Two mathematical models, namely the continuous moving-bed model (steady-state model) and the intermittent moving-bed model (transient model), have been used to describe simulated moving-bed adsorption separation processes. Four-column and 12-column simulated moving-bed systems for the separation of optical isomers with nonlinear adsorption isotherms were studied with the two models, respectively. The model equations were solved by using the numerical method of orthogonal collocation in finite elements. For the 4-column simulated moving bed, the differences between the simulation results from the two mathematical models are very obvious. Process dynamics, i.e., evolution of the species concentrations in the extract and raffinate and the axial profiles at different times, of the above systems in one switching period at the cyclic steady state are presented and discussed. They were numerically simulated with the intermittent moving bed model. The computations in a Gray J916 computer were very time consuming for the 12-column system.