This paper describes the properties of electrophoretic moving boundaries in systems containing multivalent weak electrolytes where the Kohlrausch regulating law is not valid. It is shown that zones of unexpected properties can be formed in such systems and that the adjusted concentrations in these zones cannot be predicted using present knowledge. A theoretical approach to the properties of such "non-Kohlrausch" systems is presented that allows the explanation and prediction of their properties. The theory based on velocity diagrams describes the electrophoretic evolution of a concentration boundary between a pair of zones (differing only in the concentration ratio of their components) as the formation of two moving boundaries migrating in opposite directions. The concentration profiles and velocities of these moving boundaries, that can be either sharp or broadening by electromigration dispersion, as well as the adjusted concentrations in the formed intermediate zones can be predicted from calculated velocity diagrams. Such zones differ from normal systems in that their adjusted concentrations are a function of the composition of both zones that formed the original boundary. The theory is illustrated and verified by both computer simulations and experiments.