Abstract It is anticipated that the Pierre Auger Observatory can be used to detect cosmic neutrinos of >10 19 eV that arrive at very large zenith angles. However, showers created by neutrino interactions close to the detector must be picked out against a background of similar events initiated by cosmic ray nuclei. As a step towards understanding this background, we have made the first detailed analysis of air showers recorded at Haverah Park (an array which used similar detectors to those planned for the Auger Observatory) with zenith angles above 60°. We find that the differential shower rate from 60° to 80° can be predicted accurately when we adopt the known primary energy spectrum above 10 17 eV and assume the Quark Gluon String model (QGSJET) and proton primaries. Details of the calculation are given.