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We have made the first measurements of the 330 GHz J = 3--2 lines of /sup 13/CO in the molecular clouds OMC-1 and NGC 2264. Simple velocity gradient calculations can give a consistent description of the intensities of these lines, together with the available CO (J = 2--1) isotopic lines and the equivalent J = 1--0 transitions. They indicate fractional /sup 13/CO abundances similar to those found in dark clouds, but low values of the molecular hydrogen density, n(H/sub 2/)roughly-equal5 x 10/sup 3/ cm/sup -3/. The higher densities (approx.10/sup 5/ cm/sup -3/) indicated by other molecular observations of these clouds suggest either the presence of high density fragments within the clouds or that the simple analysis is not appropriate for the CO lines, and more complex models are required to explain all the observations.