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The EGRET instrument on the Compton Gamma-Ray Observatory has detected hard-spectra gamma-ray bursts with energies as high as $10^{10}$ eV and with no evidence of spectral softening. Extensive air shower arrays could detect such bursts if the bursts' spectra extend to ultra-high-energies ($\sim 10^{14}$ eV), provided the bursts are not cosmological in origin. Using data from the CYGNUS array, we have searched on various timescales for evidence of emission of ultra-high-energy radiation coincident with over 100 gamma-ray bursts listed in the second BATSE catalog, as well as with other bursts observed by the third Interplanetary Network of satellites. Results of the search, as well as the implications on the origins of the bursts, will be presented.