  In this work the double vector meson production in ultraperipheral heavy ion
collisions is investigated within the BFKL approach. The integrated cross
sections and event rates for the processes AA --> V1 V2 AA (V_i = rho, omega,
phi, J/Psi, Upsilon) are computed and theoretical estimates for scattering on
both light and heavy nuclei are given for energies of RHIC and LHC.
