We report on the characterization of resistive switching devices based on epitaxial CeO2 thin films as a functional material. CeO2 epitaxial thin films were grown by the pulsed laser deposition technique on conductive substrates. Platinum and titanium nitride top electrodes (TE) were successively deposited. Very good performances, in terms of resistivity switching and multilevel operation capability, were obtained using the Pt TE. The dependence of the low resistance and high resistance state on the TE material and on the CeO2 film thickness were explained. The electrical characteristics of these heterostructures make them promising as synapse for neuromorphic computation, but suggest also their use with multi-valued digital systems or multibit memory cells.