  We study the analytic structure of partial-wave amplitudes derived from u-
and t-channel exchange processes. The latter plays a crucial role in
dispersion-theory approaches to coupled-channel systems that model final state
interactions in QCD. A general spectral representation is established that is
valid in the presence of anomalous thresholds, decaying particles or
overlapping left-hand and right-hand cut structures as it occurs frequently in
hadron physics. The results are exemplified at hand of ten specific processes.
