A composite model of hadrons with off-mass-shell constituent quarks was proposed earlier. We apply this model to the calculation of σ(γγ-->ρ0ρ0) 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 ρ0 has also been given.