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 and type of interaction. We show that the bound for muon poor showers in the 105 − 107 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. © 1997 American Physical Society.