Abstract
A composite model of hadrons with off-mass-shell constituent quarks was proposed earlier. We apply this model to the calculation of $\ensuremath{\sigma}(\ensuremath{\gamma}\ensuremath{\gamma}\ensuremath{\rightarrow}{\ensuremath{\rho}}^{0}{\ensuremath{\rho}}^{0})$ in the lowest order. This yields an enhancement of the cross section near threshold, as has been also experimentally seen. Similar other consequences of the model for photon-photon collisions for the other vector-meson pairs have also been given. It appears that near threshold, the vector mesons will be transversely polarized 4 times as often as they are longitudinally polarized in their c.m. frame of reference. The angular distribution of the pions from ${\ensuremath{\rho}}^{0}$ has also been given.
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