In this paper we discuss oscillation theory for linear Hamiltonian
systems for which we do not impose the controllability (or equivalently normality)
assumption. Based on the Sturmian separation and comparison theorems
on a compact interval, derived earlier by the author for these systems, we classify
them as oscillatory or nonoscillatory. Moreover, we provide comparison
theorems for such oscillatory and nonoscillatory systems. One of the goals of
this paper is to provide several examples illustrating this new theory.