Conversion of a CO2-H-2 mixture in the presence of metal-carbonaceous support catalysts (M-CS), where M is Co, Ni, Fe, and Cu, and CS is activated nonwoven carbon material (carbon felt) or other carbonaceous materials, was studied. The influence of the support and the active catalyst component on the parameters of the process was revealed. It was shown that the Co and Ni catalysts were selective for methane and that the Fe and Cu catalysts reduced carbon dioxide to carbon monoxide with 100% selectivity. Some features of the adsorption Of CO2 on these supported metal catalysts were determined with the use of the CO2 temperature-programmed desorption technique.