In the present paper we first show the experimental Raman, infrared, and neutron INS spectra of tribromomesitylene (TBM) measured in the range 50-3200 cm(-1) using crystalline powders at 6 or 4 K. Then, the bond lengths and angles determined by neutron diffraction using a TBM single crystal at 14 K are compared to the computed ones at different levels of theory. Anharmonic computations were then performed on the relaxed structure using the VPT2 approach, and for the lowest normal modes, the HRAO model has led to a remarkable agreement for the assignment of the experimental signatures. A particularity appears for frequencies below 150 cm(-1), and in particular for those concerning the energy levels of "hindered rotation" of the three methyl groups, they must be calculated for one-dimensional symmetrical tops independent of the frame vibrations. This fact is consistent with the structure established by neutron diffraction: the protons of the methyl groups undergoing huge "libration" motions are widely spread in space. The values of the transitions between the librational levels determined by inelastic neutron scattering indicate that the hindering potentials are mainly due to intermolecular interactions different for each methyl group in the triclinic cell.