  It is shown that a chiral quark model of the Nambu--Jona-Lasinio type can be
used to describe "soft"-momenta parts of the amplitudes with large momentum
transfer. As a sample, the processes \gamma^* --> \gamma (\pi,\eta,\eta') where
one of the photons, \gamma^*, has large space-like virtuality is investigated.
The \gamma^* --> \gamma (\pi,\eta,\eta')$ transition form factors are
calculated for a wide region of transferred momenta. The results are consistent
with the calculations performed in the instanton-induced chiral quark model and
agree with experimental data. The distribution amplitudes of pseudoscalar
mesons are derived.
