Methane activation in the absence of molecular oxygen over metallo-catalysts has been recognized as a potential catalytic process. In the present study, the density-functional theory (DFT) is employed to theoretically explore the mechanism of the nonoxidative dehydrogenation of methane on acid-promoted metal (Mo or W) oxides and carbide/zeolite catalysts. Various possible models of the catalyst are proposed. The structures of intermediate fragments together with CHx species that adsorbed on the catalysts were optimized and analyzed. The results suggest that the transition metal species located on the bridged hydroxyl groups, Si(OH)Al of zeolites, is the activation center competent to cleave C-H bonds. Methane activation proceeds through the initial overlap of electron density of methane with vacant d-orbitals of the metallo-center of the catalyst, followed by the formation of a transition state in which a H-H bond distance is noticeably shortened. At last, a hydrogen molecule is eliminated and a bound carbene is then shaped. The H-2 evolution sequence can be described in a stepwise reaction: CH4 + catalyst --> H4C-catalyst --> H2C-catalyst + H-2. The transition state of the adsorbed methane has a three-center-two-electron (2e-3c) bond, which is believed to be a key feature during the cleavage of two C-H bonds in the dehydrogenation process. The adsorbed CHx species on the models of catalyst MoCx[Si(O)Al] are comparable to pseudo-carbonium ions; Despite of the apparent differences in later stages, the initial steps in the dehydrogenation of methane on the MOxCy/HZSM-5 (M = Mo or W) catalysts share intrinsic properties with those of methane activation reactions in superacids.