We have observed experimentally and modeled theoretically a previously unidentified nonequilibrium state in superconducting tunnel junctions. The state occurs in small gap, multiple tunneling junctions, and is caused by the raising in energy of the quasiparticle distribution through multiple cycles of sequential forward- and back-tunneling events. Because of the low-energy gap, quasiparticles may survive in the higher-energy states until they reach the energy threshold for emission of Cooper pair-breaking phonons, leading to generation of further quasiparticles. We modeled the process by solving the coupled system of kinetic equations for interacting quasiparticles and phonons, and studied the effect experimentally in high quality Al and Ta/Al superconducting tunnel junctions in the temperature range 40–300 mK. The distinctive features are large subgap currents exceeding that due to thermal excitations by several orders of magnitude at low temperatures, together with a very sharp onset of current with bias voltage