  We consider small perturbations of the Laplace operator in a
multi-dimensional cylindrical domain by second order differential operators
with periodic coefficients. We show that under certain non-degeneracy
conditions such perturbations can open a gap in the continuous spectrum and
give the leading asymptotic terms for the gap edges. We also estimate the
values of quasi-momentum at which the spectrum edges are attained. The general
machinery is illustrated by several new examples in two- and three-dimensional
structures.
