In this paper, we present numerical simulations of the radiance and the degree of linear polarization of light reflected by the terrestrial atmosphere in the O2 A absorption band, around 760 nm. Since the O2 A band is often used to derive cloud parameters, we included clouds in our model atmosphere. The simulations show that the polarization of the reflected light changes across the O2 A band, and that this change depends strongly on the spectral resolution of the instrument. The polarization of reflected light induces errors in radiances derived from observations by polarization sensitive instruments. For the Global Ozone Monitoring Experiment (GOME) satellite instrument, which measures radiances with about 0.4-nm spectral resolution in the O2 A band, broadband polarization measurements are used to correct the narrowband radiance observations for the instrument's polarization sensitivity. Although such correction schemes significantly improve the accuracy of derived radiances in the continuum, they do not account for changes of the polarization in narrow absorption bands, such as the O2 A band. The main purpose of this paper is to investigate for cloudy atmospheres the errors in the derived radiances due to polarization changes across the O2 A band, both for a polarization sensitive instrument with a high spectral resolution and for a GOME-like resolution. If no correction scheme is used, it is found that for nadir viewing directions, the maximum errors in the absorption band can increase by up to about 20% with decreasing width of the spectral response function when the instrument's sensitivity for radiation polarized perpendicularly to the principal plane is twice as large as that for radiation polarized parallel to this plane. If, in this case, a correction scheme based on the broadband value of the polarization is used, the radiance errors can still be up to 18% with a high spectral resolution and of the order of a few percent with a GOME-like resolution. ¿ 2000 American Geophysical Union