  At high energies the saturation effects associated to the high parton density
should modify the behavior of the observables in proton-nucleus and
nucleus-nucleus scattering. In this paper we investigate the saturation effects
in the nuclear $J/\Psi$ production and estimate the modifications in the energy
dependence of the cross section as well as in the length of the nuclear medium.
In particular, we calculate the ratio of $J/\Psi$ to Drell-Yan cross sections
and show that it is strongly modified if the high density effects are included.
Moreover, our results are compared with the data from the NA50 Collaboration
and predictions for the RHIC and LHC kinematic regions are presented. We
predict an additional $J/\Psi$ suppression associated to the high density
effects.
