A 150-component, dynamic electrophoresis simulator was developed and applied to the description of capillary isoelectric focusing (CIEF) of amphoteric substances in quiescent solution. The simulator is shown to be capable of producing high-resolution pH 3-10 focusing data with 140 individual carrier ampholytes (20/pH unit) and at current densities that are used in CIEF, i.e., under conditions that were hitherto unaccessible by dynamic computer simulation. Having a focusing capillary of 5-cm length, the predicted focusing dynamics for amphoteric dyes obtained at a constant voltage of 1500 V (300 V/cm) are shown to qualitatively agree with data obtained by whole-column optical imaging. The simulation data provide detailed insight into the dynamics of the focusing process for the cases with the focusing column being sandwiched between 40 mM NaOH (catholyte) and 100 mM phosphoric acid (anolyte) or having the column ends only permeable for OH- and H+ at cathode and anode, respectively. Simulation data reveal that the number of sample boundaries migrating from the two ends of the column to the focusing positions is always equal to the number of sample components. The number of detectable migrating sample boundaries, however, can be lower. Whole-column optical imaging is demonstrated to be the method of choice for following the approach to equilibrium. With that detection format, transient sample peaks can be recognized and properly identified. This would also be possible with a scanning detector moving rapidly and repeatedly along the column but cannot be accomplished by a stationary detector placed at a specified location. The data presented demonstrate that the model together with imaging monitoring can be used to optimize the CIEF separation conditions.