We have performed density functional calculations to investigate the bimolecular CH4 + NOx (x=1, 2) and the trimolecular NO + CH4 + NO2 reactions which can be assumed to occur in the vicinity of an active site on a de-NOx catalyst. We have shown that the trimolecular reactions can take place very smoothly on a singlet energy hypersurface, while the bimolecular reactions producing unstable radicals are not favorable. We have explained these results with the high energy of the reaction products in the bimolecular reactions and the formation of HNOx molecules yielding negative stabilization energy in the trimolecular reactions with the extra NOx molecules which can be considered as spin traps in these processes. We present the geometrical changes together with the electronic changes occurring in the reactions, The significance of this study is that we could demonstrate that the increased concentration of the reaction partners due to an active site of the catalyst allows reactions which otherwise would be unlikely.