An underwater acoustic sensor array spanning ~1500 km^3 is used to search for cosmic-ray neutrinos of ultra-high energies (UHE, E > 10^18 eV). Approximately 328 million triggers accumulated over an integrated 130 days of data taking are analysed. The sensitivity of the experiment is determined from a Monte Carlo simulation of the array using recorded noise conditions and expected waveforms. Two events are found to have properties compatible with showers in the energy range 10^24 to 5x10^24 eV

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... d 10^22 to 5x10^22 eV. Since the understanding of impulsive backgrounds is limited, a flux upper limit is set providing the most sensitive limit on UHE neutrinos using the acoustic technique.