The activation of C-H bonds in different hydrocarbons on the surfaces of metal oxide and metal catalysts is considered. On oxides, it appears that the initial activation may occur through either homolytic or heterolytic scission of the C-H bond, but the reaction is surface-catalysed, The activation of methane requires highly basic sites which are susceptible to severe poisoning by carbon dioxide. With metal surfaces, the extent of oxidation of the surface can strongly affect the oxidation activity. For rhodium catalysts, it is shown that the intrinsic activity for methane combustion is high. However, rhodium is strongly deactivated under oxidising conditions when alumina is used as the support: deactivation is not observed when the support is zirconia. Transient effects on the activity of an alumina-supported palladium catalyst are reported and these show that the steady state is not easily established. Water severely inhibits the methane combustion reaction on palladium, and chlorine and sulphur dioxide are strong poisons. In contrast, for the combustion of propane on alumina-supported platinum catalysts, sulphur dioxide is a significant promoter of the reaction.