The nuclear spin relaxation of Xe-131 in methanol has been studied by means of molecular dynamics (MD) simulation, using an all-atom model for methanol. Comparison is made between a united-atom and an all-atom description of the methyl group in methanol. The source of relaxation for Xe-131 is the quadrupolar interaction, and it is triggered by fluctuations in the electric field gradient (EFG) at the quadrupolar nucleus. The time correlation function for the electric field gradient at the site of xenon (EFG-TCF) has been calculated. The effect of molecular cross-correlation in the EFG-TCF is found to be important. The principal frame of the EFG tenser is calculated, and the EFG-TCF is described as fluctuations in the:eigenvalues and reorientation of the principal axes system of the EFG tenser. It is found that the quadrupolar interaction is reduced by a fast vibrational averaging in the EFG. On time scales longer than this vibrational averaging the EFG-TCF is determined by reorientational motions in the EFG ellipsoid. The EFG-TCF can to a good approximation be described by motions in the asymmetric principal component alone, given a suitable convention. From analogous analysis of MD simulations of Xe-131 in carbon tetrachloride and water, the results are found to be transferable to Xe-131 in other solvents.