  We obtain the horizontal air shower rate from the (EeV) high energy neutrino
flux predicted in some topological defect scenarios as the source for the
highest energy cosmic rays. Emphasis is made on the different character of the
events depending on the neutrino flavor an type of interaction. We show that
the bound for muon poor showers in the $10^5-10^7$ GeV energy range is violated
by maximal predictions for superconducting cosmic string neutrino fluxes, we
compare it to other neutrino flux limits and we discuss the future of such
measurements to further constrain these models.
