  Let H = -(1/m(x))L be the reduced wave operator defined on the N-dimensional
Euclidean space, where \f L is the Laplacian. Here m(x) is a positive step
function with possible countably infinte surfaces of discontinuity (separating
surfaces) under the compatibilty condition (1.12) on each separating surface.
These compatibily condition allows us to treat the cases, among others, the
separating surfaces are cylinders. The case where the separating surface has
only one connected component was discussed in [9]. Also the case where the
separating surface is cone-shaped was considered by Eidus [6] and others ([10],
[11]). We shall prove the limiting absorption principle for H. Also we shall
discuss the case where m(x) is perturbed by a short-range or long-range
function.
