We investigate the nonlinear behavior of anodic nickel dissolution reaction coupled to hydrogen ion reduction for different cathode sizes. In a standard three-electrode cell, transpassive nickel dissolution in sulfuric acid exhibits bistable and oscillating current states when an external resistance is added in series to the working electrode. We observed bistable and oscillating currents without any external resistance in a two-electrode (cathode-anode) cell. The oscillations are interpreted by the linear polarization resistance of the cathode reaction, hydrogen reduction on nickel surface; this resistance exhibited a maximum against cathode size. Those cathodes with resistances close to the maximum stimulated strong oscillations in the cell current. Theoretical considerations implied that such maximum differential resistance cannot be interpreted with elementary Butler-Volmer kinetics but require complex, multiroute reactions. Numerical model simulating coupled anode and cathode reactions reproduced the salient dynamical features of the cathode-anode cell configuration.