We present an efficient method for the direct solution in the time domain of the equations of a novel recently proposed non-Markovian quantum-classical approximation, valid well beyond the applicability limits of both Redfield theory and Fermi's Golden Rule formula. The method is based on an ab initio molecular dynamics description of the classical bath and is suitable for applications to systems with a fairly large number of quantum levels. A simple model of the breathing sphere in a Lennard-Jones fluid was used to compare the results of the quantum-classical and purely classical treatments of vibrational energy relaxation. (C) 2003 American Institute of Physics.