- Abstract A number of solutions are presented, mostly numerical, of boundary value problems for the Nernst-Planck-Poisson equations, describing the electro-diffusional transfer of ions in electrolyte solutions adjacent to ion-selective membranes. In the locally electroneutral limit, commonly employed in electrochemistry, all these solutions exhibit the classical concentration polarization behavior with a complete saturation of the voltage current curves at high voltages. It is stressed, following an earlier publication , that deviations from local electroneutrality, which develop in the course of concentration polarization and which are reflected in the model by replacing the local electroneutrality condition by the full Poisson equation, lead to a lack of true saturation of the voltage-current curves. A class of first order surface reaction type boundary conditions at the membrane is postulated, which provide, in the locally electroneutral limit, unique, stable steady solutions of the Nernst-Planck equations with characteristics concentration polarization properties. At the same time, deviations from local electroneutrality in the region adjacent to the membrane lead, for the boundary conditions of this class, to an electrodiffusional instability of the steady solutions of the Nernst-Planck-Poisson system above a certain critical voltage.