The theory of ionic transport processes in an ion-exchange membrane electrodialysis system was developed. The fundamentals of this theory are expressed by the overall mass transport equation of ions and a solution across a membrane pair. This equation includes the overall transport number;, overall permeability coefficient it, overall electro-osmotic coefficient Phi and overall concentration-osmotic coefficient p. These parameters indicate the characteristics of an ion-exchange membrane pair placed in an electrolyte solution containing more than two kinds of ions. These parameters were measured by the electrodialysis of an electrolyte solution. The overall mass transport equation was introduced from the non-equilibrium thermodynamics. Consequently lambda, mu, Phi and p were supported by the conventional parameters defined in the non-equilibrium thermodynamics. The extended overall mass transport equation were introduced from the overall mass transport equation by adding the terms of solution leakage across the ion-exchange membranes. The solution leakage in practical-scale electrodialyzers were estimated using the extended overall mass transport equation. Solution leakage includes those moving from desalting cells to concentrating cells and those moving from concentrating cells to desalting cells. The effects of current density and linear velocity in desalting cells on the solution leakage were discussed. Furthermore, the solution leakage in electrodialyzers operating in salt-manufacturing plants were discussed. Solution leakage in large-scale electrodialyzers was recognized to be considerable, so that the influence of the leakage on the mass transport across the membrane pair is not negligible. (C) 2004 Elsevier B.V. All rights reserved.