Using PBE+U we have investigated the structural and magnetic properties of low-index Cu 2 O and CuO surfaces as well as their bulk oxides. Comparing various possible spin configurations we found that CuO prefers being antiferromagnetic, while for Cu 2 O the diamagnetic configuration is most stable. For the lowindex Cu 2 O surfaces, we observed a correlation between the stoichiometric ratio R Cu/O and the magnetic moments of the surface atoms. If there is an excess of oxygen atoms on the surface, the surface atoms have a magnetic moment with the ferromagnetic structure being the most stable. Otherwise, the respective surfaces are diamagnetic as the Cu 2 O oxide itself. In order to investigate the observed surface ferromagnetism in more detail, we calculated the spin polarized DOS and performed a Bader charge analysis. For the ferromagnetic O-excess Cu 2 O surfaces we observed additional spin-down states near the Fermi level or the conduction band minimum. These states can be assigned to the surface atoms and lead to half-metallic behaviour in the former case. Furthermore, the DOS calculations reveal a 2p-3d hybridization between the oxygen and copper atoms for all investigated surfaces as well as for the corresponding bulk phases. The Bader charge analysis demonstrates that Cu-excess Cu 2 O surfaces generally exhibit an excess of electrons at the surface compared to the bulk phase, while O-excess Cu 2 O surfaces have a deficiency of electrons at the surface compared to the bulk phase. Similar to Cu 2 O, we observed a correlation between the stoichiometric ratio and the magnetic moments of the surface atoms for the low-index CuO surfaces. If there is an excess of copper atoms on the surface, all or some of the outermost Cu atoms have no magnetic moment, although all the bulk-like Cu atoms have a magnetic moment, as in CuO itself. On the other hand, if there is an excess of oxygen atoms on the surface, the outermost Cu atoms have a magnetic moment, which is lower than in the bulk phase. By investigating different arrangements of these magnetic moments we found that the antiferromagnetic structure has the lowest surface energy and is therefore the most stable for all CuO surfaces. The Bader charge analysis of the CuO surfaces shows that the charge of the outermost Cu atoms of the Cu-terminated CuO surfaces is similar to the charge of the Cu atoms in the Cu 2 O bulk phase, which indicates that these Cu atoms are reduced (from Cu 2+ to Cu + ). Furthermore, the Bader charge analysis indicates that the Cu atoms transfer a maximum of 1.1 e, regardless of their coordination environment, and thus no Cu atom reaches a higher oxidation state than that in CuO. To study the stability of the copper oxide surfaces we used the ab initio atomistic thermodynamics approach. The resulting surface phase diagram for the Cu In conclusion, we presented a correlation between the structural and magnetic properties of different terminated copper oxide surfaces and offer a possible explanation for the observed magnetism within a simplified model. In addition, this work offers insights into the surface structure of copper-based catalysts and forms the basis for further investigations of catalytic reactions on copper oxide surfaces.