The quantum efficiency and current and voltage responsivities of fast hot-electron photodetectors, fabricated from superconducting NbN thin films and biased in the resistive state, have been shown to reach values of 340, 220 A/W, and4×104&hthinsp;V/W,respectively, for infrared radiation with a wavelength of 0.79 &mgr;m. The characteristics of the photodetectors are presented within the general model, based on relaxation processes in the nonequilibrium electron heating of a superconducting thin film. The observed, very high efficiency and sensitivity of the superconductor absorbing the photon are explained by the high multiplication rate of quasiparticles during the avalanche breaking of Cooper pairs. ©1998 American Institute of Physics.