  The current status of the muon anomalous magnetic moment (AMM) problem is
briefly presented. The corrections to the muon AMM coming from the effects of
hadronic light-by-light (LbL) scattering due to light quark-antiquark exchange
in pseudoscalar and scalar channels are estimated within the nonlocal chiral
quark model (N$\chi$QM). Within this approach the full kinematic dependence on
the photon and meson virtualities are taken into account. As a result, the
meson exchange contributions to the muon AMM calculated within N$\chi$QM are,
in general, smaller than the contributions obtained within other models. The
contribution from the scalar channel is positive and small, but stabilizes the
combined with pseudoscalar channel result with respect to variation of the
model parameters.
