  We extend a result on renormalized oscillation theory, originally derived for
Sturm-Liouville and Dirac-type operators on arbitrary intervals in the context
of scalar coefficients, to the case of general Hamiltonian systems with block
matrix coefficients. In particular, this contains the cases of general
Sturm-Liouville and Dirac-type operators with block matrix-valued coefficients
as special cases.
  The principal feature of these renormalized oscillation theory results
consists in the fact that by replacing solutions by appropriate Wronskians of
solutions, oscillation theory now applies to intervals in essential spectral
gaps where traditional oscillation theory typically fails.
