We have obtained 12 CO and 13 CO J=1-0 observations of the nearby spiral galaxy M33 to try to resolve the long-standing discrepancy between 12 CO/ 13 CO line ratios measured in Galactic giant molecular clouds and external galaxies. Interferometer maps of the molecular cloud MC20 give a 12 CO/ 13 CO line ratio of 7:52:1, which agrees reasonably well with the line ratio measured in Galactic giant molecular clouds. In contrast, the 12 CO/ 13 CO line ratio obtained from single dish data is 10:0 0:9, signiicantly higher than Galactic values but in good agreement with line ratios measured in other galaxies. The interferom-eter map of MC20 reveals that the cloud has similar spatial and velocity extents in the two lines, and thus the high single dish line ratio cannot be due to diierent lling factors in the two lines. In addition, the single dish data show no evidence for signiicant variations in the line ratio with metallicity, which eliminates abundance changes as the explanation for the high single dish line ratio. We conclude that the high 12 CO/ 13 CO line ratios observed in M33, and in the disks of spiral galaxies in general, are due to the presence of a population of diiuse molecular clouds. We obtain a lower limit to the 12 CO/ 13 CO line ratio in the diiuse molecular clouds of 13 5. The lower limit to the fraction of the total 12 CO emission from M33 that originates in the diiuse clouds is 3030%, while the upper limit is 60%. We have combined our line ratios with published measurements of the 12 CO J=2-1 to J=1-0 line ratio to determine the 12 CO and 13 CO column densities to within an order of magnitude, but the density and the temperature of the gas are not well constrained by these measurements. We estimate that diierences in the physical conditions in diiuse and giant molecular clouds are unlikely to cause the overall molecular gas mass calculated for the central kiloparsec of M33 to be in error by more than a factor of two.