Abstract Reversible one-ion and opposite-sign, two-ion univalent transfers from aqueous to organic phases (and the reverse processes) have been analyzed. Solutions of transport and interfacial potential difference equations are given in terms of concentration-distance-time profiles, potential difference vs. time chronopotentiograms and expressions for transition times when they exist. Six cases include supporting electrolyte and non-supporting electrolyte examples. One of these: two-ion, salt transport without supporting electrolyte is the Nernst-Riesenfeld example from which the ideas of electrosorption-desorption arise. Real systems investigated by Gavach and co-workers have received special emphasis.