  We study in this paper an abstract class of Klein-Gordon equations: \[
\p_{t}^{2}\phi(t)- 2\i k \p_{t}\phi(t)+ h \phi(t)=0, \] where $\phi: \rr\to
\cH$, $\cH$ is a (complex) Hilbert space, and $h$, $k$ are self-adjoint, resp.
symmetric operators on $\cH$. We consider their generators $H$ (resp. $K$) in
the two natural spaces of Cauchy data, the energy (resp. charge) spaces. We do
not assume that the dynamics generated by $H$ or $K$ has any positive conserved
quantity, in particular these operators may have complex spectrum. Assuming
conditions on $h$ and $k$ which allow to use the theory of selfadjoint
operators on Krein spaces, we prove weighted estimates on the boundary values
of the resolvents of $H$, $K$ on the real axis. From these resolvent estimates
we obtain corresponding propagation estimates on the behavior of the dynamics
for large times. Examples include wave or Klein-Gordon equations on
asymptotically euclidean or asymptotically hyperbolic manifolds, minimally
coupled with an external electro-magnetic field decaying at infinity.
