This paper reports an investigation on the role of transition-metal ions in producing ferromagnetism in CeO2 nanoparticles by electron paramagnetic resonance (EPR). Several samples of CeO2 nanoparticles annealed at 200, 300, 400, and 500 degrees C, doped with 5% Ni and 5% Co ions, characterized by X-ray diffraction (XRD), X-ray photoelectron spectroscopy (XPS), thermogravimetry analysis (TGA) and mass spectroscopy (MS), were investigated by X-band EPR at 4, 10 and 300 K, and by magnetometry at 300 K. Magnetic properties and EPR/FMR (Ferromagnetic Resonance) spectra of these nanoparticle samples were found to depend strongly on the annealing temperature (T(A)), oxygen stoichiometry, and dopant-ion species. Different behavior of saturation magnetization in the samples with the dopants, Co and Ni, is found to be due to different-inward and outward-surface diffusion of these impurity ions, respectively, during annealing. A detailed simulation of EPR/FMR spectra of isolated Co and Ni ions carried out here provides in-depth details on the role of the doped ions and oxygen (O-) defects played in the observed magnetic properties.