We present a systematic perturbation theory, extendable in principle to all orders of magnitude, for the solution of the equations of motion of an ideal Josephson element shunted by a resistance and driven by a dc current source and a small time‐dependent source. We present second‐order results for the case in which the time dependence is that of a single sinusoid, and these results are compared with other numerical and analytical calculations. Near, but not on, the first constant voltage step where the perturbation theory appears divergent, the current‐voltage characteristic is calculated by means of a nonperturbative adiabatic procedure. The impedance and responsivity agree with earlier results.