  We study characteristic features of the eigenvalues of the Wilson-Dirac
operator in topologically non-trivial gauge field configurations by examining
complete spectra of the fermion matrix. In particular we discuss the role of
eigenvectors with real eigenvalues as the lattice equivalents of the continuum
zero-modes. We demonstrate, that those properties of the spectrum which
correspond to non-trivial topology are stable under adding fluctuations to the
gauge fields. The behavior of the spectrum in a fully quantized theory is
discussed using QED_2 as an example.
