  We study possible saturation effects in the total cross-section describing
interaction of ultrahigh energy neutrinos with nucleons. This analysis is
performed within the two approaches, i.e. within the Golec-Biernat W\"usthoff
saturation model and within the scheme unifying the DGLAP and BFKL dynamics
incorporating non-linear screening effects which follow from the
Balitzki-Kovchegov equation. The structure functions in both approaches are
constrained by HERA data. It is found that screening effects affect
extrapolation of the neutrino-nucleon total cross-sections to ultrahigh
neutrino energies $E_{\nu}$ and reduce their magnitude by a factor equal to
about 2 at $E_{\nu} \sim 10^{12}GeV$. This reduction becomes amplified by
nuclear shadowing in the case of the neutrino-nucleus cross-sections and
approximate estimate of this effect is performed.
