  The spectral properties of a class of non-selfadjoint second order elliptic
operators with indefinite weight functions on unbounded domains $\Omega$ are
investigated. It is shown that under an abstract regularity assumption the
nonreal spectrum of the associated elliptic operator in $L^2(\Omega)$ is
bounded. In the special case that $\Omega=R^n $decomposes into subdomains
$\Omega_+$ and $\Omega_-$ with smooth compact boundaries and the weight
function is positive on $\Omega_+$ and negative on $\Omega_-$, it turns out
that the nonreal spectrum consists only of normal eigenvalues which can be
characterized with a Dirichlet-to-Neumann map.
