Chromatography is increasingly being used for large-scale preparative separation of precious biological components such as recombinant proteins and DNA. Several kinds of mathematical models are used to describe the liquid chromatography process. The aim of this work is investigations of existing empirical models and their numerical simulation in order to approximate experimental results in the domain of Ion-Exchange Chromatography separation. The experimental data have been interpreted according to equations derived from a theoretical model, or alternatively fitted to an empirical relation. The drawback of an empirical model, which has been found to suit a particular system, is that it is likely that the found empirical coefficients vary with the experimental conditions. However, it is important to recognize that an agreement between experiments and theory does not imply, that the theory is correct. In order for the theory to be acceptable, it must be consistent with the general physical knowledge. For this purpose two principal column morphologies were compared for the separation of Cytochrome C and α-Chymotrypsynogen two proteins found in the bovine Heart and bovine Pancreas, respectively. The columns of interest were a column packed with porous particles and a monolith column. Both are strong cation exchangers. Polydiallyl-dimethylammonium chloride) (PDADMAC), a linear cationic polyelectrolyte was investigated in the purpose of further displacement separation. Different adsorption equilibrium model have been investigated. The Langmuir adsorption equilibrium model was validated for the two cation-exchange columns as well as for the proteins and displacer molecules. A Langmuir model was found to fit well the adsorption protein data on ion-exchangers, but only under fixed elution buffer conditions (the buffer concentration, pH). The model is unable to describe the dependence on salt concentration in the elution buffer. During the displacement separation a high concentration of counter-ions is observed. This induced salt gradient can produce dramatic changes in the behavior of ion-exchange displacement. The Langmuir formalism cannot be explicitly accounted. Other equilibrium adsorption model of the interest was the Steric Mass Action (SMA) model. The SMA formalism is a three-parameter model of ion exchange designed specifically for representation of multicomponent protein-salt equilibrium in ion exchange chromatography. The model has been applied primary to simulate non-linear displacement chromatography of proteins using low molar mass displacers. The values of the SMA parameters were found to be independent of mobile phase compositions. The parameters were determined for two proteins and displacer. Experimental isotherms for the polyelectrolyte and proteins were compared with those simulated by the SMA model. Displacement chromatography, a very delicate mode of separation, was also applied to the particle-based and monolith column. Various separation conditions have been investigated.