The electron paramagnetic resonance of Ce3+ ions in ceria is a rather controversial issue. In this report we analyze the EPR line with g similar to 1.97 in the absorption spectra of ceria powders, which has been assigned in many studies to Ce3+ ions. Such an assignment is not in agreement with the experimental data nor with the theory of spin-lattice relaxation of rare earth ions in solids. Our statement is supported by our experimental results based on EPR spectroscopy of nanocrystalline ceria, synthesized in various ways, as well as by magnetization measurements of as-prepared and vacuum-annealed ceria nanoparticles. The possible model of the paramagnetic center, which is assigned to the EPR line with g similar to 1.97 in ceria, is an electron trapped near the surface Ce3+/Ce4+ redox pair.