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We calculate the contribution of semi-hadronic states with pseudoscalar$P=\pi^0, \eta$ and scalar ($\sigma$(550))meson accompanied with real photon asan intermediate state of a heavy photon to the anomalous magnetic moment ofmuon. We consider the intermediate states with $\pi_0$ and $\sigma$ as ahadrons in frames of Nambu-Jona-Lasinio model. The contribution of$\pi_0\gamma$ state is in agreement with results obtained in previoustheoretical considerations as well as with experimental data$a_\mu^{\pi_0\gamma}\approx 4.5 \times 10^{-10}$, besides we estimate$a_{\mu}^{\eta\gamma}=0.7 \times 10^{-10}, a_{\mu}^{\sigma\gamma} \sim 1.5\times 10^{-11}, a_{\mu}^{\pi^+\pi^-\gamma} \sim 3.2 \times 10^{-10}.$ Wediscass as well the LbL mechanism with $a_{\mu}^{lbl}=10.5 \cdot 10^{-10}.$

Contributions of semi-hadronic states $P\gamma;S\gamma, \pi^+\pi^-\gamma$ to amm of muon, in frames of Nambu-Jona-Lasinio model