The dissociation of CH4 and CO,, as well as the reaction between CH4 and CO,, has been investigated over supported Rh in a fixed-bed continuous-flow reactor. The decomposition of methane on rhodium occurred above 423 K, when transient evolution of hydrogen and ethane were observed. The deposition of different kinds of carbon species was established, which led to the termination of the decomposition. The reactivity of surface carbon towards hydrogen exhibited a great variance, and sensitively depended on the conditions of its formation. The dissociation of CO, was detected by infrared spectroscopy only above 523 K, and it was promoted by the presence of CH4. The reaction between CO, and CH4 proceeded rapidly above 673 K to give CO and H, with different ratios. No decay in the activity of Rh catalysts was experienced, and only very little, if any, carbon deposition was observed. The effects of different supports on all of the above processes have been examined.