For pt.I see ibid., vol.11, no.12, p.2595 (1981). Using a tailored quadrature method to solve the kinetic equation for a non-equilibrium superconductor perturbed by SIS tunnelling, the possibility of multiple gap states is explored. It is found that above a threshold bias voltage two locally stable gaps appear, the competition between which can give rise to a first-order phase transition. As the voltage is increased still further the normal state becomes the stable state. The results show a slight disagreement with the earlier work of Schon and Tremblay (1979).