  Asymptotic time evolution of a wave packet describing a non-relativistic
particle incident on a potential barrier is considered, using the Wigner
phase-space distribution. The distortion of the trasmitted wave packet is
determined by two time-like parameters, given by the energy derivative of the
complex transmission amplitude. The result is consistent with various
definitions of the tunneling time (e.g. the B\"{u}ttiker-Landauer time, the
complex time and Wigner's phase time). The speed-up effect and the negative
dispersion are discussed, and new experimental implications are considered.
