  We obtain several averaging lemmas for transport operator with a force term.
These lemmas improve the regularity yet known by not considering the force term
as part of an arbitrary right-hand side. Two methods are used: local variable
changes or stationary phase. These new results are subjected to two non
degeneracy assumptions. We characterize the optimal conditions of these
assumptions to compare the obtained regularities according to the space and
velocity variables. Our results are mainly in $L^2$, and for constant force, in
$L^p$ for $1<p \leq 2$.
