As a model of chemical reactions that take place in the active site of methanol dehydrogenase, the molecular mechanism for the oxidation of methanol by the coenzyme PQQ (pyrroloquinolinequinone) has been characterized by different theoretical methods : AM1 and PM3 semiempirical procedures, ab initio method at 3-21G, 6-31G, and 6-31G** basis set levels, second order Moller-Plesset perturbation method and calculations based on density functional theory. We examine three possible molecular mechanisms. The first two reaction pathways are based on the nucleophilic attack of methanol oxygen on both quinone groups of PQQ An analysis of a modified version of More O’Ferrall-Jencks diagrams shows that the overall process is a stepwise mechanism. : AM1 and PM3 semiempirical procedures, ab initio method at 3-21G, 6-31G, and 6-31G** basis set levels, second order Moller-Plesset perturbation method and calculations based on density functional theory. We examine three possible molecular mechanisms. The first two reaction pathways are based on the nucleophilic attack of methanol oxygen on both quinone groups of PQQ An analysis of a modified version of More O’Ferrall-Jencks diagrams shows that the overall process is a stepwise mechanism.