Combining a multi-molecular-beam approach and in situ time-resolved IR reflection absorption spectroscopy (TR-IRAS), we investigate the kinetics of methanol oxidation on a well-defined supported Pd model catalyst. The model catalyst is prepared under ultra-high-vacuum (UHV) conditions by I'd deposition onto a well-ordered Al2O3 film grown on NiAl (110). In previous studies, this system has been characterized in detail with respect to its geometric and electronic structure and its adsorption properties. Crossing molecular beams of methanol and oxygen on the sample surface, we systematically probe the rate of total methanol oxidation to CO2 as a function of surface temperature and reactant fluxes. The results are compared with equivalent experiments for the related CO oxidation reaction. Pronounced differences are observed in the kinetics of the two processes, both under steady state and under transient conditions. The dissimilarities can be related to the dehydrogenation step of methanol, which is found to be strongly inhibited at high oxygen coverage. At low oxygen fluxes, CO is formed as the main product of methanol decomposition. Via a three-beam isotope-exchange experiment combined with TR-IRAS, the kinetics of CO formation is investigated as a function of reactant fluxes and surface temperature. Mean-field simulations of the kinetics are performed in a two-step procedure. First, the kinetics of CO oxidation is described, both under steady state and transient conditions. In a second step the microkinetic model is extended to include the formation of CO formed by methanol dehydrogenation. A comparison with the experimental data indicates that the transient kinetics cannot be fully described by a mean-field approach.