The influence of the energy-dependent density of states on the collisional relaxation of highly vibrationally excited molecules is analyzed in non-reactive systems. An integral equation is solved to construct transition probability, which satisfies detailed balance and is normalized to unity at all initial energies from zero to infinity. Transition probabilities are obtained for a multiexponential model with an energy-dependent density of states. (C) 2010 Elsevier B.V. All rights reserved.