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[en] The High Altitude Water Cherenkov (HAWC) Gamma-ray Observatory is an extensive air shower detector operating in central Mexico that has recently completed its first two years of full operations. If for a burst like GRB 130427A at a redshift of 0.34 and a high-energy component following a power law with index 1.66, the high-energy component is extended to higher energies with no cutoff other than that from extragalactic background light attenuation, HAWC would observe gamma-rays with a peak energy of ∼300 GeV. This paper reports the results of HAWC observations of 64 gamma-ray bursts (GRBs) detected by Swift and Fermi, including 3 GRBs that were also detected by the Large Area Telescope (Fermi-LAT). An ON/OFF analysis method is employed, searching on the timescale given by the observed light curve at keV–MeV energies and also on extended timescales. For all GRBs and timescales, no statistically significant excess of counts is found and upper limits on the number of gamma-rays and the gamma-ray flux are calculated. GRB 170206A, the third brightest short GRB detected by the Gamma-ray Burst Monitor on board the Fermi satellite (Fermi-GBM) and also detected by the LAT, occurred very close to zenith. The LAT measurements can neither exclude the presence of a synchrotron self-Compton component nor constrain its spectrum. Instead, the HAWC upper limits constrain the expected cutoff in an additional high-energy component to be less than for reasonable assumptions about the energetics and redshift of the burst.