Doping ZnO with rare earth and 4d transition elements is a popular technique to manipulate the optical properties of ZnO systems. These systems may also possess intrinsic ferromagnetism due to their magnetic moment borne on 4f and 4d electrons. In this work, the structural, electronic, and magnetic properties of Eu- and Pd-doped ZnO were investigated by the ab initio density functional theory methods based on generalized gradient approximation. The relative stability of incorporation sites of the doped elements in the ZnO host lattice was studied. The ground state properties, equilibrium bond lengths, and band structures of both the ZnO:Eu and ZnO:Pd systems were also investigated. The total and partial densities of electron states were also determined for both systems. It was found that in the ZnO:Eu system, ambient ferromagnetism can be induced by introducing Zn interstitial which leads to a carrier-mediated ferromagnetism while the ZnO:Pd system possesses no ferromagnetism.PACS 31.15.E-, 75.50.Pp, 75.30Hx.