We report results from 120 hours of livetime with the Goldstone Lunar Ultra-high energy neutrino Experiment (GLUE). The experiment searches for ≤ 10 ns microwave pulses from the lunar regolith, appearing in coincidence at two large radio telescopes separated by 22 km and linked by optical fiber. Such pulses would arise from subsurface electromagnetic cascades induced by interactions of ≥ 100 EeV neutrinos in the lunar regolith. No candidates are yet seen, and the implied limits constrain several current models for ultra-high energy neutrino fluxes.In 1962, G. Askaryan predicted that electromagnetic cascades in dense media should produce strong coherent pulses of microwave Cherenkov radiation [1]. Recent confirmation of this hypothesis at accelerators [2] strengthens the motivation to search for such emission from cascades induced by predicted high energy neutrino fluxes, closely related to the measured fluence of ≃ 10 20 eV cosmic rays in many models.Two such models, the Z-burst model [3], and a generic class known as Topological Defect (TD) models [4], predict ultrahigh energy (UHE) neutrinos with either monoenergetic or very hard energy spectra. In the Z-burst model, UHE neutrinos annihilate with relic cosmic background neutrinos via the νν → Z 0 channel. The Z 0 then decays rapidly in a burst of hadronic secondaries which create the observed ∼ 10 20 eV cosmic rays. The need to match the observed UHE cosmic ray fluxes and satisfy the current constraints on neutrino masses (which modify the annihilation resonance energy) then lead to a requirement on minimal neutrino fluxes at the resonance energy near 10 22−23 eV. The Z-burst model thus formally requires only neutrinos at a single energy, with no specification for how such a flux might be produced.The Z-burst model is also significant in that it is a variation on an earlier idea [5] in which the νν annihiliation process could be used as a probe of the cosmic background neutrinos, one of the few viable ways ever proposed for detection of these relic cosmological neutrinos-it requires only a sufficient flux of UHE neutrinos and a detector with the sensitivity to measure them. Constraints on these UHE ν fluxes thus can rule out this potential detection channel for the relics, in addition to excluding their role in UHE cosmic ray production.TD models, in contrast, postulate a very massive relic particle from the early universe which is decaying in the current epoch and producing secondaries observed as UHE cosmic rays. The required masses approach the Grand-Unified Theory (GUT) scale at ∼ 10 24 eV, and the decay products thus have a very hard spectrum extending up to the rest mass energy of the particles. Because of these very hard spectra, detectors optimized for lower-energy neutrinos, even up to PeV energies, do not yet constrain these models, and new approaches, such as the experiment we report on here, are required.Neutrinos with energies above 100 EeV (1 EeV = 10 18 eV) can produce cascades in the upper 10 m of the lunar regolith resulting in pulses that are...