By means of a network thermodynamic treatment, the non-stationary ionic transport in membranes was studied. A network model based on the time-dependent version of the Nernst-Planck flux equations is proposed for a thin permeable membrane between two solutions of NaCl-HCl at different concentrations. With this network model and the electrical circuit simulation program PSPICE, the response of such a membrane system to step current input is reported in terms of the time and space changes in concentrations, electric field and ionic fluxes. The method is quite general and extremely efficient, permitting treatments of multi-ion systems whatever the boundary and experimental conditions may be.