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We obtain the horizontal air shower rate from the (EeV) high energy neutrinoflux predicted in some topological defect scenarios as the source for thehighest energy cosmic rays. Emphasis is made on the different character of theevents depending on the neutrino flavor an type of interaction. We show thatthe bound for muon poor showers in the $10^5-10^7$ GeV energy range is violatedby maximal predictions for superconducting cosmic string neutrino fluxes, wecompare it to other neutrino flux limits and we discuss the future of suchmeasurements to further constrain these models.Comment: 15 pages Latex file and 5 PS figures. Uses Revtex and epsfig.st

Limits on Topological Defect Neutrino Fluxes from Horizontal Air Shower Measurements