Аннотация:The search for downward-going and Earth-skimming ultrahigh energy cosmic neutrinos by the Surface Detector array of the Pierre Auger Observatory (PAO) is analyzed in a framework of the Arkani-Hamed–Dimopoulos–Dvali (ADD) model with n large extra dimensions under the assumption that the diffuse neutrino flux dNν/dEν has the form
(kE^{−2}_ν in the energy range (10^17)(–2.5)×10^19 eV. The upper bound on the flux normalization k is obtained in the ADD model, taking into account that no neutrino events were found at the PAO. It is shown that for some values of n and (n+4)-dimensional Planck scale M_D our bound on k is more stringent than that of the Pierre Auger collaboration. The lower bound on M_D as a function of n is obtained.