Quasielastic light scattering consisting of two components has been observed in single crystals of rutile (TiO{sub 2}). The broad component with a linewidth of 330 GHz at 297 K becomes narrower with decreasing temperature. In contrast, the narrow component, which has a linewidth of 1.1 GHz at 297 K, broadens as the temperature decreases. We present a unified explanation for both components, which is based on two-phonon difference Raman scattering. For the narrow component, it will be shown that two-phonon difference processes from a {ital single} acoustic phonon branch explain the temperature dependence of the intensity and the wave vector dependence of the linewidth at low temperatures. The conventional explanation in terms of entropy-fluctuation scattering is also attempted for temperatures above 200 K where phonon collisions occur more frequently than at lower temperatures and the phonon system may be considered hydrodynamically. For the broad component, two-phonon difference scattering from {ital different} phonon branches will be shown to provide a good explanation for the temperature dependent intensity. Furthermore, temperature dependence of the linewidth and its insensitivity to changes in scattering wave vector are also explained with this model. {copyright} {ital 1999} {ital The American Physical Society}