The adsorption of the molecules CO, CO2, and H2 on several ceria and zinc oxide surfaces was studied by means of periodical DFT calculations and compared with infrared frequency data. The stable CeO2(111), CeO2(331), and ZnO(0001) perfect faces were the first substrates considered. Afterwards, the same surfaces with oxygen vacancies and a ZnO monolayer grown on Ceria(111) were also studied in order to compare the behaviors and reactivities of the molecules at those surfaces. The ceria surfaces were substantially more reactive than the ZnO surface towards the CO2 molecule. The highest adsorption energy for this molecule was obtained on the CeO2(111) surface with oxygen vacancies. The molecules CO and H2 both presented low or very low reactivities on all of the surfaces studied, although some reactivity was observed for the adsorption of CO onto the surfaces with oxygen vacancies, whereas H2 exhibited reactivity towards the CeO2(111) surface with oxygen vacancies. This work was performed to provide a firm foundation for novel process development in methanol synthesis from carbon oxides, steam reforming of methanol for hydrogen production, and/or the water-gas shift reaction.