  We study the rho^0 and phi decays into pi^+ pi^- gamma, pi^0 pi^0 gamma and
phi into pi^0 eta gamma using a chiral unitary approach to deal with the final
state interaction of the M M system. The final state interaction modifies only
moderately the large momenta tail of the photon spectrum of the rho^0 --> pi^+
pi^- gamma decay. In the case of phi decay the contribution to pi^+ pi^- gamma
and pi^0 pi^0 gamma decay proceeds via kaonic loops and gives a distribution of
pi pi invariant masses in which the f_0(980) resonance shows up with a very
distinct peak. The spectrum found for phi --> pi^0 pi^0 gamma decay agrees with
the recent experimental results obtained at Novosibirsk. The branching ratio
for phi --> pi^0 eta gamma, dominated by the a_0(980), is also in agreement
with recent Novosibirsk results.
