  The process of exclusive vector meson production (gamma gamma to J/psi rho^0)
is studied for almost real photons. This process may be reduced to
photoproduction of J/psi off the rho^0 meson. We discuss the possibility of
extracting the gluon distribution of rho^0 and of the photon from such
measurement. Predictions are also given for the reaction (e+e- to e+ e- J/psi
rho^0) for various e+e- cms energies typical for LEP and for the future linear
colliders.
