Controlled semi-classical approximations for the evolution kernels (the propagators) of the Wigner function in the cases of tunneling and propagation in dispersive media are derived. The semi-classical propagators follow well defined trajectories determined by the local group velocity and a path delay which is a multi-dimensional generalization of Wigner phase-delay time. A comparison between exact and semi-classical time evolution gives good agreement for propagation in dispersive media if the harmonic term in the dispersion relation is the dominant term and excellent agreement for deep tunneling. (C) 2004 Elsevier B.V. All rights reserved.