Photodissociation phenomena are described within a quantum-classical treatment based on the partial Wigner transform of the density matrix and its Liouville-von Neumann equation. Two basic approximations are introduced, to convert the equations into forms readily integrable by numerical methods. Results are presented for the NaI ferntosecond time evolution of quantum populations, coherence, position and momenta averages and their dispersion, and for the time evolution of a grid of points in phase space corresponding to a bundle of trajectories. Comparing with exact results, it is concluded that the procedure gives correct results over long times, and properly accounts for the coupling of very different (quasibound and nearly free) atomic motions. (C) 2004 Elsevier B.V. All rights reserved.