Studies of structural and magnetic properties of Co-, Kr-, and Ar-implanted ZnO were performed by means of X-ray diffraction and SQUID magnetometry. Magnetization was measured at the same conditions prior and after implantation. For each kind of applied ions, implantation was carried out for two selected, as a result of preliminary calculations, fluences. In Co implanted ZnO, thin layer magnetization measurements revealed the appearance of the Brillouin-kind paramagnetic phase accompanied by some residual ferromagnetic/superparamagnetic contribution. The magnetic moment equal to about 1.7 µB per implanted Co ion in the case of implantation with higher dose of 4 × 10 16 cm −2 and about 2.1 µB in the case of implantation with lower dose of 2 × 10 16 cm −2 Co ions was observed. On the other hand, no changes in magnetization were observed as a result of implantation for Kr-or Ar-implanted ZnO. Thus, we could not find any evidence that irradiation damages caused by Kr and Ar ions, in the range of ion energies and fluences used by us, could result in magnetic response.