The linear sweep and large amplitude ac voltammetric responses of ion-exchange membrane systems have been numerically investigated in the limiting current regime. The system under study is constituted by a cation-exchange membrane and two diffusion boundary layers on both sides of the membrane. The ionic transport processes are theoretically prescribed by the Nernst-Planck flux equations, the electrical neutrality condition, and the Donnan equilibrium relations at the membrane/solution interfaces. The transport parameters have been chosen from an experiment on linear sweep voltammetry in a standard cation-exchange membrane in contact with a NaCI solution. An original numerical study on linear sweep voltammetry and large amplitude ac voltammetry in ion-exchange membrane systems is presented by using a network simulation method. The study focuses on the weakly nonlinear regime by ignoring the dynamics of the diffuse charge at the interfacial regions. Some of our results provide new insights in relation to the threshold values of the sweep rate and the frequency above or below which the transient electric current through the system is higher than the steady-state limiting current. (C) 2014 Elsevier B.V. All rights reserved