By combining molecular beam techniques and time-resolved infrared reflection absorption spectroscopy (TR-IRAS) we have studied the kinetics of the CO oxidation reaction on an alumina-supported Pd model catalyst. The Pd particles are deposited by metal evaporation under ultrahigh vacuum conditions onto a well-ordered alumina film, prepared on a NiAl(110) single crystal. Particle size, density, and structure of the Pd deposits have been characterized in previous studies. In the low temperature region, transient and steady-state experiments have been performed over a wide range of CO and oxygen fluxes by crossing two effusive molecular beams on the sample surface. We determine the steady-state CO2 production rate as a function of the CO fraction in the impinging gas flux. Simultaneously, the occupation of CO adsorption sites under steady-state conditions is monitored by in situ infrared spectroscopy. The origin of different types of CO2 transients is discussed. In particular we focus on the transient CO2 production after switching off the CO beam. For the model catalyst investigated, detailed reaction rate measurements in combination with TR-IRAS show that the origin of the particular transient behavior of the supported model system is not due to the presence of specific adsorption sites on small particles, as has been proposed previously. Instead, we suggest that the transient behavior is a consequence of the inhibition of the dissociative adsorption of O-2 at high CO coverage. Additionally, the inherent heterogeneity of the supported particle system can enhance the observed effect.