Solutions of the simplified time-dependent Nernst-Planck electrodiffusion equations for various membrane models under the influence of a step voltage change are presented. Comparison of the results for a membrane with continuous sites to those for membranes with two, three, or five intermediate sites shows little difference either qualitatively or quantitatively in the concentration of the diffusible ion inside the membrane, although some quantitative differences are evident in the calculate currents. The Nernst-Planck equations (1) have been used extensively to describe electrolyte processes in membranes. While exact solutions to these equations for steady-state processes have been obtained (2), solutions of the time-dependent equations, which result from a perturbation of the system, have so far required some simplification to permit solution (3,4). In all of these cases, one tacit assumption is that the membrane is continuous, i.e., the diffusing ions can occupy any position along the path through the membrane. Such an assumption is inherent in the use of the Nernst-Planck equations.In this paper we present a comparison between the results expected from one simplified version of the Nernst-Planck equations in continuous form and the same simplified processes with the ion motion treated as a discrete, random walk process. The latter treatment has not been used extensively in this area and could prove important, especially in the treatment of thin membranes such as those found in biological systems. Continuous (macroscopic) model In the formulation of the problem, several simplifying assumptions were made. The diffusion coefficient (D), the electric mobility (U , and the electric field (E = -bV/bx) were all assumed to be independent of the position of the ion in the membrane. Inherent in the last assumption is that a pseudoneutrality exists, i.e., the Poisson term is treated as insignificant. The final constraint simplifying these equations is that the potential is a step function: V = Vo, t < 0. V = V, t > 0.[1A] [iB] With these assumptions, the Nernst-Planck equations be-