We study interference patterns in the &fgr; → (&ggr;a0+ &pgr;0&rgr;) → &ggr;&pgr;&eegr; and &fgr; → (&ggr;f0+ &pgr;0&rgr;) → &ggr;&pgr;0&pgr;0reactions. Taking into account the interference, we fit the experimental data and show that the background reaction does not distort the &pgr;0&eegr; spectrum in the decay &fgr; → &ggr;&pgr;&eegr; everywhere over the energy region and does not distort the &pgr;0&pgr;0spectrum in the decay &fgr; → &ggr;&pgr;0&pgr;0when the invariant massm&pgr;0&pgr;0> 670 MeV. We discuss the details of the scalar meson production in the radiative decays and note that there are conclusive arguments in favor of the one‐loop mechanism &fgr; →K+K−→ &ggr;a0(or &ggr;f0). We discuss also distinctions between the four‐quark, molecular, and two‐quark models and argue that the establishment of the scalar meson production mechanism in the &fgr; radiative decays gives new strong evidence in favor of the four‐quark nature of the scalara0(980) andf0(980) mesons. © 2002 American Institute of Physics