The theory of ionic transport processes in ion-exchange membrane electrodialysis system was developed. The fundamentals in this theory is expressed by the overall mass transport equation of ions and a solution across a membrane pair. The equation includes overall transport number lambda, overall diffusion coefficient mu, overall electro-osmotic coefficient phi and overall osmotic coefficient rho. 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 seawater. Parameters lambda, mu and phi were expressed by empirical functions of rho. These functions facilitate the simulation of the electrodialytic process. Parameter rho was found to have the relation to non-equilibrium parameter; filtration coefficient L-p. The formulas were obtained in order to express various aspects such as the transport of ions and solutions across membranes, electrolyte concentration in both a desalting and concentrating cell, desalting ratio of a desalted solution and current efficiency. Ionic constituents in a concentrated solution were also measured by the seawater electrodialysis. The relationship between current density and the equivalent ratio of ions in a concentrated solution was expressed by empirical formulas. Thereby, the concentration of Na+, K+, Mg2+, Ca2+, Cl- and SO42- ions in a concentrated solution was estimated. The voltage applied to a cell pair is known to be related to electrical resistance and membrane potential. The electrical resistance of solutions in a cell pair was determined by the specific resistance measurement of electrolyte solutions. The direct current electrical resistance of membranes in a cell pair was measured by the seawater electrodialysis. The effect of concentration polarization on the voltage applied to a cell pair is seen in the direct current resistance of the membrane. Energy consumption during the process of seawater electrodialysis was evaluated using the function of the voltage applied to a cell pair. The energy consumption, the limiting current density and the saturation current density are discussed on the basis that the current density and solution velocity (electrolyte concentration) in desalting cells are distributed in an electrodialyzer. (C) 2003 Elsevier Science B.V. All rights reserved.