Problems of steady-state and non-steady-state multi-component ion transport through ion-exchange and bipolar membranes and adjacent diffusion layers are considered. Equations of material balance of electrolyte components and the Poisson equation are used as the mathematical model. An efficient numerical method providing splitting of equations of material balance of electrolyte components and the Poisson equation is proposed. The method requires no explicit consideration of interfaces and the use of Dorman equations; it provides exact fulfillment of boundary conditions both for the mode of constant current density and for the mode of constant voltage. The following results of simulating the ion transport through ion-exchange and bipolar membranes and adjacent diffusion layers are presented: the distributions of concentrations, electrical potential, charge, and partial current densities and the voltammograms of electromembrane systems. (c) 2005 Elsevier B.V. All rights reserved.