When a superconductor is subjected to electromagnetic radiation, characteristic quantities such as the magnitude of the gap may assume higher values than those assumed under equilibrium conditions. Intensive theoretical and experimental studies of this so-called superconductivity stimulation have culminated in many insights and a puzzle: the resulting state is unstable with respect to infinitesimal fluctuations. A resolution to this problem is proposed here in the form of a moving condensate. Derivation and solution of the appropriate kinetic equation yields a family of locally stable states supporting finite superfluid velocity and current. These findings can be tested experimentally with existing techniques.