A semi-empirical approach to treat, predict and scale transfer characteristics of electrodialysis (ED) and electrodeionization (EDI) stacks used for the desalination of dilute solutions in overlimiting current modes is described. The approach is based on the recent theoretical ideas about the mechanisms of overlimiting current transfer in membrane systems. In particular, electroconvection and exaltation effects are discussed. For scaling, the similarity theory and compartmentation method are used. As a result, relatively simple equations are obtained, which describe the ED (EDI) characteristics (the mass transfer coefficient, the Sherwood number, the degree of desalination and others) as functions of four parameters: the inlet concentration, the solution flow rate, the potential drop over a cell pair and the length of desalination channel. The comparison of experimental measurements and calculations is examined for several types of ED and EDI stacks: without filling or containing non-conducting spacer, ion-exchange bed or profiled membranes. (C) 2008 Elsevier B.V. All rights reserved.