We study the radiative ρ, ω and 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. Other mechanisms in which two kaons are produced through the same sequential mechanisms or from vector meson decay into two kaons which undergo final state interaction leading to the final pair of pions or π0η, are also considered. The results of the parameter free theory, together with the theoretical uncertainties, are compared with the latest experimental results at Frascati and Novosibirsk.