  The constraints followed from gauge invariance and analyticity are considered
for the amplitudes of radiative transitions of composite systems when composite
systems are treated in terms of spectral integrals. We discuss gauge-invariant
amplitudes for the transitions S -> gamma S and V -> gamma S with scalar S and
vector V mesons being two-particle composite systems of scalar (or
pseudoscalar) constituents, and we demonstrate the mechanism of cancellation of
false kinematical singularities. Furthermore, we explain how to generalize the
performed consideration for quark-antiquark systems, in particular, for the
reaction phi(1020) -> gamma f0(980). Here we also consider in more detail the
quark-model non-relativistic approach for this reaction.
