The Schrödinger operator H = -Δ + V is considered in a layer or in a d-dimensional cylinder. The potential V is assumed to be periodic with respect to a lattice. The absolute continuity of H is established, provided that V ∈ 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 a cylinder. Bibliography: 14 titles.