Chromatographic processes provide a powerful tool for the separation of multicomponent mixtures in which the components have different adsorption affinities. As an alternative to conventional batch chromatography as a discontinuous process, the simulated moving bed (SMB) process as a continuous chromatographic separation process gained more and more impact recently. Mathematical modelling and simulation of batch chromatographic processes is widely documented in the literature. For the modelling of SMB chromatographic processes two different strategies exist. The first one considers the corresponding true moving bed process neglecting the cyclic switching and thus the dominating dynmics of the process. The second alternative which is considered within this framework is to connect dynamic models of single chromatographic columns while considering the cyclic port switching in order to represent the dynamics of the real process correctly. We here describe three different approaches for the modelling and simulation of chromatographic separation processes with nonlinear adsorption thermodynamics described by the Langmuir isotherm. The first one is a rigorous modelling and numerical simulation approach, the second one is based on the equilibrium theory and proceeds from the analytical solution for binary separation processes based on nonlinear wave propagation. The third approach only includes nonidealities caused by the limited mass transfer Fates. All approaches are analyzed and compared with respect to complexity, accuracy and computational time.