Dynamic input-output-models have been identified for columns of an industrial sequential ion-exclusive chromatographic separation unit. Models are aimed at describing motion and form transformation of the fronts of different substances in the columns so that changes in "limit cycles" dynamics and drifts to undesired disturbed states could be observed on-line with model based simulations. The model structure has been innovated on the basis of classical Wiener representation, in which nonlinear dynamic system is described with a combination of linear Laguerre dynamics and static nonlinear mapping. The static mapping is realized here with MLP-type neural network. A separate delay model is needed for describing the movement of the front. The delay time adapts on variations of the process flow rate. Form transformation of the front is described with a dispersion model, which is smoother type Wiener-MLP model. Forward and backward Laguerre presentations are calculated with Laguerre filters. These Laguerre presentations are mapped to the output with a neural network. Dynamics of "salt" and two important compounds have been modeled on the basis of analyzed samples, which were taken in a factory experiment during normal production. A priori information about the process dynamics can be included in the dispersion model by choosing a suitable Laguerre parameter, but otherwise representativeness of the identification data determines validity of the model.