A theoretical model to describe the spectral response of SIS tunnel junctions under irradiation in the presence of diffusion and edge losses of non-equilibrium quasiparticles has been developed. The model takes into account the back-tunnelling effect, in the general case of asymmetrical rates of tunnelling, gamma(12) not equal gamma(21). It provides a quantitative estimate of parameters like the edge reflectivity, the diffusion length and the diffusion coefficient, which are important parameters for a diagnostic of STJ-detectors. The predictions of the theory are compared with an experimental spectrum obtained from a Nb-based STJ. (C) 2000 Elsevier Science B.V. All rights reserved.