  The energy--zenith angular event distribution in a neutrino telescope
provides a unique tool to determine at the same time the neutrino-nucleon cross
section at extreme kinematical regions, and the high energy neutrino flux. By
using a simple parametrization for fluxes and cross sections, we present a
sensitivity analysis for the case of a km^3 neutrino telescope. In particular,
we consider the specific case of an under-water Mediterranean telescope placed
at the NEMO site, although most of our results also apply to an under-ice
detector such as IceCube. We determine the sensitivity to departures from
standard values of the cross sections above 1 PeV which can be probed
independently from an a-priori knowledge of the normalization and energy
dependence of the flux. We also stress that the capability to tag downgoing
neutrino showers in the PeV range against the cosmic ray induced background of
penetrating muons appears to be a crucial requirement to derive meaningful
constraints on the cross section.
