  The exclusive production of \pi\pi and \pi\rho in hard \gamma^{\star}\gamma
scattering in the forward kinematical region where the virtual photon is highly
off-shell are studied through the \gamma\to\pi^- Transition Distribution
Amplitudes. The calculation is based on a covariant Bethe-Salpeter approach,
applied to the Nambu - Jona-Lasinio model, for the determination of the pion
bound state. In particular it is shown that the pion pole contribution produces
a large enhancement of the differential cross section for the pion pair
production with respect to previous estimates.
