We present a quasi-elastic neutron scattering (QENS) study on the methyl group dynamics of ubiquinone Q(0) in the solid and liquid state. For solid ubiquinone Q(0), the dynamics can be described with three Lorentzian functions in the framework of a jump model among three equidistant sites on a circle. According to the known molecular structure of Q(0) in the solid state, this is consistent with three nonequivalent methyl groups in the molecule. From the temperature-dependent analysis of the QENS spectra, the activation energies were determined. The barrier heights could be evaluated from librational bands in the inelastic part of the spectra. The results from neutron spectroscopy are compared to Gaussian 03 calculations leading to an assignment of the activation energies to the different methyl groups in Q(0). The dynamics of Q(0) in the liquid state is evaluated with a scattering function taking into account three different molecular motions. It is demonstrated that the temperature dependence of the long-range diffusion and isotropic rotational diffusion exhibit an Arrhenius-like behavior, whereas the process of methyl group rotation in the liquid phase is virtually free of a barrier.