  The high parton density present at high energies and large nuclei is expected
to modify the lepton - hadron cross section and the associated observables. In
this paper we analyse the impact of the high density effects in the average
inelasticity and the neutrino - nucleus cross section at ultra high energies.
We compare the predictions associated to the linear DGLAP dynamics with those
from the Color Glass Condensate formalism, which includes non-linear effects.
Our results demonstrated that the non-linear effects reduce the average
inelasticity and that the predictions of the distinct approaches for the
neutrino - nucleus cross section at ultra-high energies are similar.
