  Let $h$ be a without fixed point lift to the plane of a homeomorphism of the
open annulus isotopic to the identity and without wandering point. We show that
$h$ admits a $h$-invariant dense open set $O$ on which it is conjugate to a
translation and we study the action of $h$ on the compactly connected
components of the closed and without interior set ${\bf R}^2 \setminus O$.
