  The hadronic corrections to the muon anomalous magnetic moment, due to the
full gauge-invariant set of diagrams with dynamical quark loop and intermediate
pseudoscalar and scalar states light-by-light scattering insertions, are
calculated in the framework of the nonlocal chiral quark model. These diagrams
correspond to all hadronic light-by-light scattering contributions to $a_{\mu}$
in the leading order of the $1/N_{c}$ expansion in quark model. The result for
the quark loop contribution is $a_{\mu}^{\mathrm{HLbL,Loop}}=\left(
11.0\pm0.9\right) \cdot10^{-10}$, and the total result is
$a_{\mu}^{\mathrm{HLbL,N\chi QM}}=\left(16.8\pm1.2\right) \cdot 10^{-10}$.
