Density functional and semiempirical (MNDO) theories are used to determine transition states and the corresponding activation barriers of hydrogen exchange and dehydrogenation of methane catalyzed by a protonated zeolite cluster model. The nonlocal density functional activation barriers were found to be 125 and 343 kJ/mol for hydrogen exchange and dehydrogenation, respectively. From the imaginary frequency of one of the transition state eigenmodes, the reaction coordinates were deduced. Additionally, from the activation barrier and vibration, rotation, and translation partition functions, reaction rate constants have been evaluated using transition state reaction rate theory.