  We show that the Auger Air Shower Array has the potential to detect neutrinos
of energies in the $10^{19}~$eV range through horizontal air showers. Assuming
some simple conservative trigger requirements we obtain the acceptance for
horizontal air showers as induced by high energy neutrinos by two alternative
methods and we then give the expected event rates for a variety of neutrino
fluxes as predicted in different models which are used for reference.
