We describe a model for photon absorption by superconducting tunnel junctions in which the full energy dependence of all the quasiparticle dynamic processes is included. The model supersedes the well-known Rothwarf–Taylor approach, which becomes inadequate for a description of the small gap structures that are currently being developed for improved detector resolution and responsivity. In these junctions relaxation of excited quasiparticles is intrinsically slow so that the energy distribution remains very broad throughout the whole detection process. By solving the energy-dependent kinetic equations describing the distributions, we are able to model the temporal and spectral evolution of the distribution of quasiparticles initially generated in the photoabsorption process. Good agreement is obtained between the theory and experiment.