  We calculate the pion pole term of the light-by-light contribution to the
$g-2$ of the muon in the framework of an effective chiral quark model with
instanton-like nonlocal quark--quark interaction. The full kinematic dependence
of the pion-photon transition form factors is taken into account. The
dependence of form factors on the pion virtuality decreases the result by about
15% in comparison to the calculation where this dependence is neglected.
Further, it is demonstrated that the QCD constraints suggested by Melnikov and
Vainshtein are satisfied within the model. The corresponding contributions
originate from the box diagram as well from the pion-pole term. Our chiral
nonlocal model result for the pion-pole light-by-light contribution to
$(g-2)/2$ of the muon is $(6.3-6.7) \cdot10^{-10}$, which is in the ball park
of other effective-model calculations.
