Our overall objective is the development of a process for large scale purification of biologicals by isoelectric focusing (IEF). Thus, it was important to gain a better understanding of the underlying physical phenomena through mathematical modeling and computer simulation of the process. A mathematical model of the steady state in IEF was developed for an L-component system of ampholytes or monovalent buffers. It is based on the fundamental equations describing the components' dissociation equilibria, mass transport due to diffusion and electromigration, electroneutrality, and the conservation of charge. The model consists of ordinary differential equations coupled to a system of algebraic equations. The validity and usefulness of these simulationshas been confirmed in the formulation of actual buffer mixtures for experimental IEF. This model was recently extended to include the transient evolution to a steady state. Furthermore the new formulation applies to other electrophoretic processes, notably isotachophoresis and zone electrophoresis. As a result, we now have the first general model which predicts the behavior of a given chemical system in a variety of electrophoretic processes.