Ceria (CeO2) is an oxygen storage material vital to the proper functioning of automobile three-way catalysts and is typically viewed as an anion conductor. Prior experimental work using temperature programmed static secondary ion mass spectrometry (TPSSIMS) has indicated that for rutile TiO2, a prototypical oxide, the mobile species are Ti cations rather than O anions. To further expand on the mobile species in CeO2 we have investigated the diffusion of both cerium and oxygen ions by TPSSIMS. The CeO2( 1 1 1) film was heteroepitaxially grown by molecular beam epitaxy on a yttria stabilized zirconia substrate. Although high quality low-energy electron diffraction patterns and Auger electron spectroscopy spectra free of impurity signals were obtained after just a few sputtering and annealing cycles, further cleaning was necessary to remove intense alkali and alkaline earth signals observed in SSIMS. The CeO2(1 1 1) surface was slightly enriched in O-18 by first annealing the film in UHV at 830 K and then exposing the 130 K crystal to O-18(2). TPSSIMS data in conjunction with temperature programmed desorption data demonstrate that surface oxygen atoms begin to exchange with the bulk around 550 K. Physical deposition of submonolayer amounts of isotopically enriched cerium (Ce-136) in an O-18(2) background allowed the simultaneous study of the diffusion of both cerium and oxygen ions. Surface cerium cations were found to be immobile with no diffusion into the bulk for temperatures up to 900 K, the highest temperature studied.