Four proton Zeeman-torsional level matching resonances were observed in the γ phase of tetrahedrally coordinated Si (CH3)4. The resonances were observed by measuring the Larmor frequency dependence of the coupling time between proton Zeeman and CH3 torsional-tunneling energy reservoirs. Two such resonances are known to occur if the potential, which hinders the angular displacements of planar CH3 oscillators, has threefold symmetry. If the hindering potential is a mixture of a strong sixfold and a weaker threefold term, seven such level matching resonances are possible. However, in only four of these cases does the dipolar interaction bring about observable fast (∼ 10 m s) polarization transfer between the saturated spin states and the torsional-tunneling states. Since the sixfold contribution to the hindering potential is caused by inter-CH3 oscillator interactions, the observation of four resonances indicates a strong torsion-torsion interaction. In general, level-matching resonance spectra and the associated magnetization fractions give clues about the ground state manifold, while the resonance linewidth and intensity contain information about CH3 dynamics. © 1991.