Earth-like, potentially habitable exoplanets are prime targets in the search for extraterrestrial life. Information about their atmospheres and surfaces can be derived by analyzing thelight of the parent star reflected by the planet. We investigate the influence of the surface albedo A s , the optical thickness b cloud ,thealtitude of water clouds, and the mixing ratio of biosignature O 2 on the strength of the O 2 A-band (around 760 nm) in theflux and polarization spectra of starlight reflected by Earth-like exoplanets. Our computations for horizontally homogeneous planets show that small mixing ratios (η<0.4) will yield moderately deep bands in flux and moderate-to-small band strengths in polarization, and that clouds will usually decrease the band depth in flux and the band strength in polarization. However, cloud influence will be strongly dependent onproperties such as optical thickness, top altitude, particle phase, coverage fraction, andhorizontal distribution. Depending on the surface albedoand cloud properties, different O 2 mixing ratios η can give similar absorption-band depths in flux and band strengths in polarization, especially if the clouds have moderate-to-high optical thicknesses. Measuring both the flux and the polarization is essential to reduce the degeneracies, although it will not solve them,especiallynot for horizontally inhomogeneous planets. Observations at a wide range of phase angles and with a high temporal resolution could help to derive cloud properties and, once those are known, the mixing ratio of O 2 or any other absorbing gas.