The surface detector array of the Pierre Auger Observatory is sensitive to ultra-high energy neutrinos in the cosmic radiation. Neutrinos can interact in the atmosphere close to ground (down-going) and, for tau neutrinos, through the Earth-skimming mechanism (up-going) where a tau lepton is produced in the Earth crust that can emerge and decay in the atmosphere. Both types of neutrino-induced events produce an inclined particle air shower that can be identified by the presence of a broad time structure of signals in the water-Cherenkov detectors. We discuss the neutrino identification criteria used and present the corresponding limits on the diffuse and point-like source fluxes.