A multipass tandem Fabry–Perot interferometer was used to measure the Brillouin light scattering in nematic polymer solutions of poly-γ-benzyl glutamate (PBG). The longitudinal acoustic phonon frequency and linewidth were determined as a function of the angle between the phonon wave vector and the nematic director. We have observed an anisotropy of 22% in sound velocity and 40% in the Brillouin linewidth in PBG nematic solutions. Our analysis indicates that elastic relaxation due to polymer concentration fluctuations is important. However, the proposed second sound wave could not be determined due to the experimental limit of the present technique.