A composite model of hadrons with off-mass-shell constituent quarks was proposed earlier. We apply this model to the calculation of sigma(..gamma gamma -->..rho/sup 0/rho/sup 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 have transverse polarization 4/5 (and longitudinal polarization 1/5) in their c.m. frame of reference. The angular distribution of the pions from rho/sup 0/ has also been given.