The reaction mechanisms of the Beckmann rearrangement (BR) of cyclohexanone oxime to e-caprolactam in the gas phase and catalyzed by mordenite are investigated. For the gas-phase reaction, starting with the protonated oxime, the rate-control ling step is the transformation of the N-protonated to an O-protonated species (1,2-H shift) with an activation energy of 178 kJ/mol. The barriers for the subsequent reaction steps of the transformation to N-protonated epsilon-caprolactam are significantly lower, 10 and 54 kJ/mol N-insertion and hydrolysis of the carbiminium ion. As possible active sites in the zeolite, Bronsted acid (BA) sites, silanol nests, and surface silanol groups are considered. The most favorable reaction path comprising three reaction barriers of 88, 64, and 40 kJ/mol for the 1,2-H transfer, the N-insertion, and the hydrolysis of the carbiminium ion has been found for a BA site. H-bonding is found to play a key role in the reaction catalyzed by weak acid sites. The activation energies for the rate-controlling step of the Beckmann rearrangement increases in order BA site (142 kJ/mol - 1,2-H shift + N-insertion) < silanol nest (184 kJ/mol - 1,2-H shift + N-insertion) < H-bonded terminal silanol groups (223 kJ/mol - N-insertion) < isolated silanol group (266 kJ/mol N-insertion). We have also used harmonic transition state theory to calculate the reaction rates for catalysis by BA sites and silanol nest. Due to the large difference in the activation energies of the individual steps, the BR catalyzed by BA sites or silanol nests behave like simple first-order reactions with effective reaction barriers of 142 and 184 kJ/mol, respectively. The reaction at BA sites is about 5 orders of magnitude faster than that at a silanol nest. However, the actual turnover of a reaction catalyzed by BA sites might by slowed by the relatively high desorption energy of the product and frequent readsorption and desorption at an increased concentration of BA sites.