  We show that future detectors of ultrahigh-energy cosmic-ray neutrinos will
be able to measure neutrino-nucleon cross section at energies as high as
10^{11}GeV or higher. We find that the flux of up-going charged leptons per
unit surface area produced by neutrino interactions below the surface is
inversely proportional to the cross section. This contrasts with the rate of
horizontal air showers (HAS) due to neutrino interactions in the atmosphere,
which is proportional to the cross section. Thus, by comparing the HAS and
up-going air shower (UAS) rates, the neutrino-nucleon cross section can be
inferred. Taken together, up-going and horizontal rates ensure a healthy total
event rate, regardless of the value of the cross section.
