Based on a study of the high resolution S-1<--S-0 fluorescence excitation spectrum of p-toluidine (p-methylaniline) and related G(12) molecules, we propose that the threefold axis of the methyl group is tilted slightly with respect to the symmetry axis of the molecular frame, and exhibits a kind of precessional motion in the course of its hindered internal rotation. We derive a new Hamiltonian to describe this motion and show that it is consistent with previous modifications of the traditional torsion-rotation Hamiltonian first proposed by Wilson, Lin, and Lide [J. Chem. Phys. 23, 136 (1955)]. Applying the new Hamiltonian to the S-1<--S-0 spectrum of p-toluidine, we have determined. the sixfold barrier heights V-6(S-0) = (-) 5.6 and V-6(S-1) = (-) 43.9 cm(-1), values that are similar to those of toluene and other 4-substituted toluenes.