  Let $V_\Gamma$ be a lattice periodic potential and $A$ and $\phi$ external
electromagnetic potentials which vary slowly on the scale set by the lattice
spacing. It is shown that the Wigner function of a solution of the Schroedinger
equation with Hamiltonian operator $H = {1/2} (-\I\nabla_x - A(\epsilon x))^2 +
V_\Gamma (x) + \phi(\epsilon x)$ propagates along the flow of the semiclassical
model of solid states physics up an error of order $\epsilon$. If
$\epsilon$-dependent corrections to the flow are taken into account, the error
is improved to order $\epsilon^2$. We also discuss the propagation of the
Wigner measure. The results are obtained as corollaries of an Egorov type
theorem proved in a previous paper (math-ph/0212041).
