Frozen-in trans and gauche conformational disorder of symmetrical difluorotetrachloroethane (DFTCE) produces the tendency of this plastic crystal to form an orientational glassy state on cooling below T(g) = 86 K. To throw light upon the freezing mechanism in DFTCE neutron diffraction and Brillouin scattering as well as infrared and dielectric measurements are employed. The overall picture of the results obtained can be characterized in terms of a classical glass-transition process with a relaxation frequency obeying the Vogel-Fulcher law. However, a more sophisticated picture of the freezing process is indicated by a quantitative analysis of the new Brillouin data, e.g. the temperature dependence of the sound velocity. The behaviour could be understood on the basis of a mode-coupling theory.