  We apply the non-local chiral quark model to study vector and axial
pion-to-photon transition amplitudes that are needed as a nonperturbative input
to estimate the cross section of pion annihilation into the real and virtual
photon. We use a simple form of the non-locality that allows to perform all
calculations in the Minkowski space and guaranties polynomiality of the TDA's.
We note only residual dependence on the precise form of the cut-off function,
however vector TDA that is symmetric in skewedness parameter in the local quark
model is no longer symmetric in the non-local case. We calculate also the
transition form-factors and compare them with existing experimental
parametrizations.
