ABSTRACTThe co-doping of hexagonal GaN with Er and O is investigated by means of density functional calculations. Predominantly Er-O defect-pairs characterized by a binding energy around 0.5 eV are formed. Different geometric configurations with various orientations (i.e. axial and basal pairs with C_3v or C_1h symmetry) are expected with similar formation energies. Independent of the particular configuration, the presence of oxygen does not deeply affect the atomic structure and the electronic charge distribution around the Er centers. The relatively high binding energy suggests that Er-O pairs should survive thermal treatment. An investigation of the binding energy per bond indicates that on the other hand Er-O_x complexes (x=2,3,4) are not likely to be formed (differently from Er-O co-doped Si). Rather, as long as the oxygen fluence does not overtake the Er fluence, different oxygen ions will be bound to different Er-centers.