According to the coupling model of relaxation, structural relaxation in glass-forming liquids is comprised of an intermolecularly uncorrelated step ("fast alpha-relaxation process") in the picosecond time range followed by a slowed, intermolecularly cooperative, "slow alpha" process. Molecular dynamics simulation data [Sindzingre, P.; Klein, M. J. Chem. Phys. 1992, 96, 4681] have shown that for the "strong" liquid methanol, the fast relaxation step is absent. This finding is in contrast to the prominent fast relaxation appearing hi fragile liquids about the glass transition temperature. The differing behavior of methanol can be accounted for from an analysis of the self part of the intermediate scattering function, F-s(k,t) according to the coupling model. The latter relates the magnitude of the fast alpha-relaxation to the relaxation time, tau*, and to the exponent beta of the slow ct-process described by the stretched exponential function exp[-(t/tau*)(beta)]. This function fits the experimental Fs(k,t) for t longer than 2 ps, The apparent absence of a fast relaxation step in methanol is shown to be a consequence of the weak intermolecular constraints governing the dynamics in "strong" liquids, a result consistent with the prominence of the fast process in polymers and other fragile glass-formers. This conclusion is supported by dielectric relaxation data (frequencies up to 90 GHz) and far-infrared data (> 150 GHz) on methanol.