  We consider the observability problem for non-autonomous evolution systems
(i.e., the operators governing the system depend on time). We introduce an
averaged Hautus condition and prove that for skew-adjoint operators it
characterizes exact observability. Next, we extend this to more general class
of operators under a growth condition on the associated evolution family. We
give an application to the Schr\"odinger equation with time dependent potential
and the damped wave equation with a time dependent damping coefficient.
