The adsorption of methanol on ordered epitaxial layers of cerium oxides grown on a Cu(lll) substrate has been studied using X-ray photoelectron spectroscopy (XPS), low-energy electron diffraction (LEED), temperature-programmed desorption (TPD), and Fourier transform reflection/absorption infrared spectroscopy FT-RAIRS) measurements. The oxide films exhibit a LEED pattern characteristic of a CeO2(111)-like structure, but the Ce/O stoichiometry achieved is strongly dependent on the exact pretreatment and film history. Grazing emission XPS also indicates that some Ce3+ ions are still present in the surface layers at 300 K after oxidation treatments. Methanol adsorbs dissociatively at 300 K, with a relatively high sticking probability, to yield surface methoxy species. The IR spectra of the methoxy species, in particular the C-O stretch frequency, provide information about their coordination to the oxide surface, the presence of surface oxygen vacancies, and the general level of oxidation of the film. The methoxy species are stable on the (Ill)-type terraces of thicker (>5 ML) oxide films to temperatures in excess of 550 K but then decompose at about 585 K to yield predominantly H-2 and CO with some simultaneous evolution of formaldehyde and water. A substantial number of more coordinatively unsaturated cerium ions exist at and near the periphery of oxide islands on films of a submonolayer oxide coverage and on aggregated films of higher oxide coverage (between 1 and 5 ML). When the substrate is well-oxidized, then some of the methoxy species adsorbed at such sites are readily oxidized to the formate species while the decomposition temperature of the remaining methoxy groups in this peripheral region is lowered to about 560 K and their decomposition yields a higher proportion of formaldehyde than is seen for the (111) terrace sites.