The current-voltage characteristics of a superconductor-normal metal junction are affected by the proximity superconductivity induced on the normal side. We study this effect using the quasiclassical theory. We first present a unified derivation of the previous results obtained by time-dependent Ginzburg-Landau (TDGL) theories. In order to study the effect beyond the scope of the TDGL theory, we approximate the induced order parameter by a step function. The amplitude and the phase of the induced order parameter as well as the width of the step are determined self-consistently. The calculation is made in the pure limit, but no restrictions are set on the temperature or on the transmission coefficient of the junction besides the ones implicit in the step approximation. A time-dependent solution for the order parameter is found at all currents or voltages. It is found that the results in the TDGL region and outside are relatively similar, although different mechanisms are responsible for the conversion from the normal to supercurrent in each case.