The two-photon decay widths of scalar mesons sigma(600), f_0(980) and a_0(980) as well a_0 -> rho(omega)gamma and f_0 -> rho(omega)gamma are calculated in the framework of the local Nambu-Jona-Lasinio model. The contributions of the quark loops (Hartree-Fock approximation) and the meson loops (next 1/Nc -approximation where Nc is the number of colors) are taken into account. These contributions, as we show, are the values of the same order of magnitude. For the f_0 decay the K-loop contribution turns out to play the dominant role. The results for two-gamma decays are in satisfactory agreement with modern experimental data. The predictions for a_0 -> rho(omega)gamma and f_0 -> rho(omega)gamma widths are given.
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