  The light-by-light contribution to the anomalous magnetic moment of muon
(g-2)_{\mu} from the hadronic exchanges in the neutral pseudoscalar meson
channel is calculated in the nonlocal chiral quark model. The full kinematic
dependence of the meson-two-photon vertices on the virtualities of the mesons
and photons is taken into account. The status of various phenomenological and
QCD short-distance constraints is discussed and the comparison with the
predictions of other models is performed. It is demonstrated that the effect of
the full kinematic dependence in the meson-photon vertices is to reduce the
contribution of pseudoscalar exchages to a_\mu ^{PS,LbL} by approximately
factor 1.5 in comparison with the most of previous estimates.
