Dielectric, magnetic and Raman measurements of cerium oxide nanoparticles obtained by the precipitation method are discussed. Morphological study was performed by scanning electron microscopy, confirming the formation of nanoparticles of 5–27 nm. The Raman spectra exhibited a strong band around 465 cm−1, corresponding to the symmetrical stretching mode of the Ce-O8 vibrational unit. The nature of the room temperature ferromagnetism of cerium oxide nanoparticles was analyzed, taking into account the oxygen defects at the surface or interface of the nanoparticles. The evolution of dielectric constant, ε′, and dielectric loss, ε″ was studied as a function of frequency at different temperatures. Additionally, the variation of the electric conductivity versus temperature was investigated. Finally, complex impedance study of the cerium oxide nanoparticles was performed.