  We discuss the spectral properties of collisional semigroups associated to
various models from transport theory by exploiting the links between the
so-called resolvent approach and the semigroup approach. Precisely, we show
that the essential spectrum of the full transport semigroup coincides with that
of the collisionless transport semigroup in any $L^p$--spaces $(1 <p < \infty)$
for three 2D--transport models with Maxwell--boundary conditions.
