The electronic structure of bare MeO and Me 2 dimers (with Me = Rh or Pd) has been calculated together with their interaction with a methane molecule for various adsorption geometries by means of quantum chemical density functional methodology. It has been found that the strongest non-dissociative adsorption of methane occurs in a bridging position on a palladium dimer accompanied by very strong activation of a C-H bond and a negligible energy barrier for the bond scission. Any adsorption on other systems was weaker and the barrier higher. This could be ascribed to the absence of repulsive 5s electrons in the case of palladium dimer. The strongest stabilization of the dissociated hydrogen was found, however, to occur on PdO. These results may be useful in explaining experimental findings which indicated that a supported palladium catalyst, showing subsequently metallic and oxidized phases is a very efficient medium for methane combustion.