The magnetic properties of transition-metal (TM)-doped n-type ZnTmO are theoretically analyzed and compared to the published experimental results. For the two most studied cases of TM = Mn, Co, we demonstrate the interest of magnetic resonance experiments for the investigation of the origin of sometimes observed ferromagnetism and paramagnetic properties in single-phase material. The conclusion is that ferromagnetism in ZnTMO is extrinsic and related to the second phase formation during the growth or after annealing. Substitutional TM (Mn, Co) in ZnO gives rise to antiferromagnetic nearest-neighbor interactions similar to the case of the other TM-doped II–VI compounds.