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. The first step corresponds to the formation of a hemiketal intermediate, the transition structure (TS1) being a four-membered ring. The second step is associated with the decomposition of this intermediate and with the formation of formaldehyde. The TS2 can be described as a six-membered ring. The third molecular mechanism is associated with the hydride and proton transfers between the methanol and both carbonylic oxygens of PQQ The corresponding transition structure (TS3) is a eight-membered ring and an analysis of a modified version of More O'Ferrall-Jencks diagrams and the transition vector for TS3 reveals an asynchronous pathway, describing this molecular mechanism as an initial hydride transfer followed by the proton transfer. The barrier heights for the three alternative reaction pathways are similar, showing that they are competitive molecular mechanisms. The geometries of the stationary structures and the transition vector associated with TSs on potential energy surfaces show many similarities and the dependence of these properties upon model systems and theoretical methods are analyzed and discussed.