We used radiative transfer calculations and model atmospheres for a theoretical investigation of the behavior of the degree of linear polarization, P, of light emerging from the top or the bottom of the cloudless atmosphere in the wavelength region of the O2 A absorption band, between 755 and 775 nm. Results of P are shown for four model atmospheres and for various albedos of the underlying Lambert surface. One of the model atmospheres contains only molecules, whereas the other atmospheres contain also aerosols. It is shown that when the molecular absorption optical thickness of the atmosphere is much smaller than one, which represents the continuum and the weak absorption lines in the band, the state of polarization of the emerging radiation is mainly determined by low-order scattering in the lowest atmospheric layers and by reflection by the surface. In the strong absorption lines, where the molecular absorption optical thickness is much larger than one, we distinguish the three following situations: (1) P of the reflected light is mainly determined by single scattering by molecules and aerosol in the upper atmospheric layers, (2) for small solar zenith and/or viewing angles, P of the diffusely transmitted light is mainly determined by single scattering, and (3) for other geometries, P of the diffusely transmitted light is predominantly due to second-order scattering, with the first scattering taking place in the upper atmospheric layers and the second in the lower layers. For a given surface albedo, the variation of P across an absorption line thus depends on the scattering properties of the atmospheric particles and on their vertical distribution. The surface albedo and P of light emerging from the atmosphere in the principal plane are shown to be related through a simple formula at each wavelength within the absorption band. It is concluded that high-resolution spectropolarimetry in wavelength regions with strongly varying molecular absorption optical thickness can provide valuable information on aerosol at various altitudes in the atmosphere. ¿ 1999 American Geophysical Union