We present a kinetic equation which is obtained after a hierarchy of approximations from the generalized electron-phonon Wigner function. The equation accounts for quantum effects in the electron-phonon interaction which are investigated by numerical experiments. An analysis shows that in contrast to the potential term, which is non local in momentum but local in space, the interaction term is non local also in the real space. (C) 2002 Elsevier Science B.V. All rights reserved.