Fast relaxation processes in the structural glass and glassy crystal of ethanol as well as in the glassy crystal of cyano cyclohexane were studied by quasielastic light scattering (LS). Depolarized and polarized LS spectra together with the Brillouin line were measured applying a tandem Fabry-Perot interferometer at frequencies 1-1500 GHz. Depolarized, polarized LS and internal friction data exhibit very similar behavior, thus reflect the same relaxations. The depolarized LS spectra are described by assuming a nearly constant loss (NCL) contribution dominating in the frequency range from 1 GHz to a few tens GHz and by a fast dynamics contribution at higher frequencies. The NCL amplitude increases exponentially with temperature in a similar way as found by dielectric spectroscopy for other molecular glasses. The data cannot be described by thermally activated dynamics in double well potentials, a result contradicting the findings in inorganic glasses such as silica. (C) 2003 American Institute of Physics.