  The analytic structure of {\it physical} amplitudes is considered for gauge
theories with confinement of excitations corresponding to the elementary
fields. Confinement is defined in terms of the BRST algebra. BRST-invariant,
local, composite fields are introduced, which interpolate between physical
asymptotic states. It is shown that the singularities of physical amplitudes
are the same as in an effective theory with only physical fields. In
particular, there are no structure singularities (anomalous thresholds)
associated with confined constituents, like quarks and gluons. The old proofs
of dispersion relations for hadronic amplitudes remain valid in QCD.
