  We develop the complex scaling for a manifold with an asymptotically
cylindrical end under an assumption on the analyticity of the metric with
respect to the axial coordinate of the end. We allow for arbitrarily slow
convergence of the metric to its limit at infinity, and prove a variant of the
Aguilar-Balslev-Combes theorem for the Laplacian $\Delta$ on functions. In the
case of a manifold with (noncompact) boundary it is either the Dirichlet or the
Neumann Laplacian. We introduce resonances as the discrete non-real eigenvalues
of non-selfadjoint operators, obtained as deformations of the Laplacian by
means of the complex scaling. The resonances are identified with the poles of
the resolvent matrix elements $((\Delta-\mu)^{-1}F, G)$ meromorphic
continuation in $\mu$ across the essential spectrum of $\Delta$, where $F$ and
$G$ are elements of an explicitly given set of analytic vectors. The Laplacian
has no singular continuous spectrum, the eigenvalues can accumulate only at
thresholds.
