We describe wave decay rates associated to embedded resonances and spectral
thresholds for manifolds with infinite cylindrical ends. We show that if the
cut-off resolvent is polynomially bounded at high energies, as is the case in
certain favorable geometries, then there is an associated asymptotic expansion,
up to a $O(t^{-k_0})$ remainder, of solutions of the wave equation on compact
sets as $t \to \infty$. In the most general such case we have $k_0=1$, and
under an additional assumption on the ends of the manifold we have $k_0 =
\infty$. If we localize the solutions to the wave equation in frequency as well
as in space, our results hold for quite general manifolds with infinite
cylindrical ends.