We study the radiative ϕ decay into π0π0γ and π0ηγ taking into account mechanisms in which there are two sequential
vector-vector-pseudoscalar or axial-vector--vector--pseudoscalar steps followed
by the coupling of a vector meson to the photon, considering the final state
interaction of the two mesons. There are other mechanisms in which two kaons
are produced through the same sequential mechanisms or from ϕ decay into
two kaons and then undergo final state interaction leading to the final pair of
pions or π0η, this latter mechanism being the leading one. The results
of the parameter free theory, together with the theoretical uncertainties, are
compared with the latest experimental results of KLOE at Frascati.Comment: 28 pages, 20 figure