In this contribution, the identification and control of nonlinear SMB-chromatographic processes are discussed. Instead of using the physical manipulated process variables, the flow rates of extract, desorbent, and recycle, and the switching time directly, a new set of input variables (β-factors) is employed as control inputs to reduce input/output couplings. A new measure of the front positions of the axial concentration profiles is used as outputs. Multi-layer neural network models are identified for this nonlinear MIMO system. The identified model is used in a model predictive control algorithm. In this algorithm a parameter varying linear model is employed which avoids the on-line computation of the nonlinear optimization problem. The simulation results show that the identified model gives a very good approximation of the process models and the LPVMPC scheme has a good control performance.