  The number of ultrahigh energy events at IceCube is estimated, for the first
time, taking into account non-linear QCD effects in the neutrino - hadron cross
section. We assume that the extragalactic neutrino flux is given by
$\Phi_{\nu}(E_{\nu})=\Phi_{0}E^{-2}_{\nu}$ and estimate the neutrino - hadron
cross section using the dipole approach and a phenomenological model for the
dipole - hadron cross section based on non-linear QCD dynamics. We demonstrate
that the non-linear prediction is able to describe the current IceCube data and
that the magnitude of the non-linear effects is larger than 20 % for visible
energies of order of 2 PeV and increases with the neutrino energy. Our main
conclusion is that the non-linear QCD effects are non-negligible and should be
taken into account in the analysis of the number of ultrahigh energy events.
