The periodic modes of a voltage-driven resonant small-junction Josephson circuit are studied by accurate numerical methods starting from large dissipation. As dissipation decreases, sections of the average current vs. voltage characteristic become unstable and new branches develop on those sections, corresponding to new modes which are exact subharmonics of the old mode. For low enough dissipation chaotic ranges of voltage occur, i.e., ranges with no stable periodic modes. This circuit is a component of many experimental circuits, e.g., finite junctions, DC and RF squids, etc., and so the behavior found here should occur widely. © 1982.