  The contribution of the QCD Pomeron to the process AA -> AA J/Psi J/Psi is
discussed. We focus on the photon-photon collision, with the quasi-real photon
coming from the Weizsacker - Williams spectrum of the nuclei. We calculate the
cross section for this process considering the solution of the LLA BFKL
equation at zero momentum transfer using a small-t approximation for the
differential cross section of the subprocess. Furthermore, the impact of
non-leading corrections to the BFKL equation is also analyzed. In both cases
the cross section is found to increase with the energy, predicting considerable
values for the LHC energies. Moreover, we compare our results with the Born
two-gluon approximation, which is energy independent at the photon level. Our
results indicate that the experimental analyzes of this process can be useful
to discriminate the QCD dynamics at high energies.
