Limits on Topological Defect Neutrino fluxes from Horizontal Air Shower measurements

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.