The quasi-elastic neutron scattering (QENS) spectra over the temperature range 10–270 K were studied. The activation energies for the stochastic jumps of methyl groups in neat tetramethylpyrazine (TMP) and in the complex TMP·TCNB (tetracyanobenzene) were estimated to be equal to 5.0 ± 1.2 and 2.2 ± 1.1 kJ/mol, respectively, which means that the methyl groups behave in the complex more freely than in TMP. This conclusion is in good agreement with frequencies of the CH3 torsional modes recorded in the inelastic neutron scattering (INS) spectra. They are also confirmed by the DFT calculations for the crystalline state of TMP and TMP·TCNB, although the calculations overestimate the effect of the crystalline state on the CH3 torsional frequencies. The difference in the behavior of the methyl groups in neat TMP and TMP·TCNB is also reflected in the blue-shift of the ν(CH) stretching vibration modes.