Using Van Hove's density correlation-function technique, the intensity spectrum of light scattered by a relaxing liquid is calculated. The treatment differs from the previous work on the subject, due to Mountain, in two respects: (a) the liquid is assumed to have a relaxing shear viscosity instead of a static shear viscosity, and (b) instead of using the time integral representation for the relaxing bulk viscosity, we consider it to arise from the relaxation of an ordering parameter and apply the thermodynamic theory of relaxation processes to calculate the correlation function. The first modification is necessary if the theory is to explain the occurrence of Brillouin components in highly viscous liquids like glycerine. The second modification gives insight into the nature of the approximations involved in using the integral representation for the bulk viscosity. Finally, it is shown that the exact expression for the spectral intensity, for our model, may be approximately written as a sum of five Lorentzians. Two of these represent the Brillouin components, and the other three form the central component.