A microscopic model for the dephasing of optical impurities in amorphous hosts such as glasses or polymers is presented. The characteristics of the host system are taken into account via two-level systems (TLS's) proposed some time ago to explain the low-temperature properties of inorganic glasses. The TLS's couple to the impurity and to the vibrational degrees of freedom of the matrix. Exact eigenvalues of the equation of motion for correlation functions describing the optical line shape are obtained. In the case of weak coupling between TLS's and impurity, and after averaging over the parameter regime characterizing the TLS's it is found that the optical linewidth depends strongly on the boundaries of this regime. At temperatures well below the Debye temperature one obtains a crossover from a quadratic to a linear temperature increase of the linewidth in the case of coupling to acoustic vibrations, and a crossover from exponential to linear for coupling to optical (librational) modes. © 1984 The American Physical Society.