  We find that in "two-photon"-like processes in the scalar $\varphi^3_E$ model
and also in hadron-pair production arising from the collisions of a real
(transversely polarized) and a highly virtual, longitudinally polarized, photon
in QCD, there is duality between two distinct nonperturbative mechanisms. These
two mechanisms, one involving a twist-3 Generalized Distribution Amplitude, the
other employing a leading-twist Transition Distribution Amplitude, are
associated with different regimes of factorization. In the kinematical region,
where the two mechanisms overlap, duality is observed for the scalar
$\varphi^3_E$ model, while in the QCD case the appearance of duality turns out
to be sensitive to the particular nonperturbative model applied and can,
therefore, be used as a tool for selecting the most appropriate one.
