The adsorption of oxygen on bcc Fe-Cr(100) surfaces with two different alloy concentrations is studied using ab initio density functional calculations. Atomic-scale analysis of oxygen-surface interactions is indispensable for obtaining a comprehensive understanding of macroscopic surface oxidation processes. Up to two chromium atoms are inserted into the first two surface layers. Atomic geometries, energies and electronic properties are investigated. A hollow site is found to be the preferred adsorption site over bridge and on-top sites. Chromium atoms in the surface and subsurface layers are found to significantly affect the adsorption properties of neighbouring iron atoms. Seventy-one different adsorption geometries are studied, and the corresponding adsorption energies are calculated. Estimates for the main diffusion barriers from the hollow adsorption site are given. Whether the change in the oxygen affinity of iron atoms can be related to the chromium-induced charge transfer between the surface atoms is discussed. The possibility to utilize the presented theoretical results in related experimental research and in developing semiclassical potentials for simulating the oxidation of Fe-Cr alloys is addressed.