The transition states of the hydrogen exchange and dehydrogenation reactions of methane on a zeolite acid site are studied within the framework of the density functional theory and the atoms-in-molecules theory. The transition state for the hydrogen exchange reaction is found to be characterized by a slightly ionic interaction between a distorted CH5+ structure and the negatively charged zeolite. No free carbocation is found. The dehydrogenation reaction presents a transition state in which three different fragments can be well identified, namely, an almost planar CH3+ structure, a H-2 pseudomolecule, and the negatively charged zeolite. The interaction between the fragments can be described as a closed-shell one, typical of rather ionic systems.