The network pseudo-thermodynamic analysis has been applied for describing competitive pertraction of divalent cations with antiported univalent (hydrogen) cations. A mathematical model to be solved numerically has been developed and used to predict the separation effects caused by nonstationary conditions for a liquid membrane transport. Numerical calculations were made in order to compute such pertraction characteristics as: input and output membrane selectivity (ratio of respective fluxes), concentration profiles for cations bound by a carrier in a liquid membrane phase, and,the overall separation factors. These quantities are discussed as dependent on time, the kinetic constants of interfacial reversible reactions, and diffusion coefficients of carrier species in a liquid membrane phase. The computations of fluxes and separation factors as dependent on time have revealed high separation efficiency of unsteady state pertraction as compared with steady or near-steady state process (with reactions near equilibrium state). According to the results of this study, the method of bond-graph network can be proposed as sufficient for modeling the processes of industrial interest and various fundamental phenomena underlying the effectiveness of synthetic and natural membranes. (C) 2003 Elsevier B.V. All rights reserved.