  We consider the Schr\"odinger operator $H = -\Delta + V$ in a layer or in a
$d$-dimensional cylinder. The potential $V$ is assumed to be periodic with
respect to some lattice. We establish the absolute continuity of $H$, assuming
$V \in L_{p, \loc}$, where $p$ is a real number greater than $d/2$ in the case
of a layer, and $p > \max (d/2, d-2)$ for the cylinder.
