We have measured the magnetization of undoped and Fe(2+/3+) doped CeO(2-y) nanocrystals at various temperatures and magnetic fields. The Stoner condition N(0)I > 1 is multiply fulfilled in the case of nano-CeO(2-y), favoring the band ferromagnetism approach. In the case of Fe-doped samples, the magnetization versus magnetic field dependence is well fitted with a weighted Langevin function. A blocking temperature of about 20 K is obtained both from the ZFC/FC curves and from the coercive field against temperature dependence. The temperature and field dependence of the magnetization clearly shows the presence of nanosized particles which exhibit superparamagnetic behavior.