Measurements on discontinuous thin gold films near the percolation threshold show that the current at which nonlinear response takes place, Iexc, scales with the conductance 0, as Iexc0x, x=1.470.10. Two possible theoretical models have been considered and studied analytically and numerically. The first is based on local nonlinear contributions from the metallic constituents. The second models nonlinear hopping or tunneling across narrow insulating bridges. Only the second model is compatible with the experiment. © 1986 The American Physical Society.