In order to gain insight into the so-called d⁰-magnetic properties of defective ZnO we have carried out first principles calculations on various types of defects formed by intrinsic defects and doped atoms as well as pairs of them. The doped atoms include N and H. In agreement with previous works we find several possibilities to create magnetic defects, especially by hole formation. Our results show that two defects which are in the vicinity of each other and that are magnetic when isolated, in general become non-magnetic if one of them is acceptor-like and the other donor-like. Furthermore, we have investigated the magnetic interaction of different defect pairs via total energy calculations, the results of which show in all cases the stability of ferromagnetic configurations. In order to reproduce the experimentally found localization of the magnetic hole states we have investigated the effect of applying correlation corrections on the p orbitals containing these holes.