  The Bethe-Salpeter equation provides the most widely used technique to
extract bound states and resonances in a relativistic Quantum Field Theory.
Nevertheless a thorough discussion how to identify its solutions with physical
states is still missing. The occurrence of complex eigenvalues of the
homogeneous Bethe-Salpeter equation complicates this issue further. Using a
perturbative expansion in the mass difference of the constituents we
demonstrate for scalar fields bound by a scalar exchange that the underlying
mechanism which results in complex eigenvalues is the crossing of a normal (or
abnormal) with an abnormal state. Based on an investigation of the
renormalization of one-particle properties we argue that these crossings happen
beyond the applicability region of the ladder Bethe-Salpeter equation. The
implications for a fermion-antifermion bound state in QED are discussed, and a
consistent interpretation of the bound state spectrum of QED is proposed.
