The eastern cloud of the nearby Cepheus complex, located at and , has been mapped in the CO() transition at a resolution of 0.8 pc with the CfA 1.2 m telescope. This massive, but fairly diffuse cloud, with visual extinction , has also been sampled in the and 21 rotational transitions of CO and at the same resolution, using the CfA and POM-2 millimeter telescopes. The radiative transfer of the lines has been treated in the LTE and LVG approximations, the two yielding comparable results. In CO, low excitation temperatures have been found in the range of , with moderate optical depths () and CO column-densities up to . In , the gas is optically thin with slightly lower excitation temperatures of , for column-densities up to . Under these conditions, the observed ratios of over velocity-integrated intensities, , have been found to be consistent with a uniform value over the cloud of in CO and in , as typical of many clouds. The ratios of CO over velocity-integrated intensities, ), have been found to decrease with intensity as expected from the progressive saturation of the CO lines. The large scatter about this relation, observed at scales of 0.8 and 0.2 pc, cannot be accounted for by instrumental error, beam dilution, or the dispersion of excitation temperatures and line widths measured in the cloud. The fluctuations are therefore indicative of intrinsic variations in the molecular abundances. In particular, very low ratios may result from efficient isotopic fractionation in this cold environment. Similar variations in intensity have been reported at a scale of 0.2 pc in two other dark clouds, HCL 2 (Cernicharo & Guélin 1987) and IC 5146 (Lada et al. 1994s), from the behaviour of their or ratios with visual extinction. Together with the present results, they suggest that the abundance integrated along the line of sight largely varies inside the diffuse envelopes of molecular clouds.