  Nematic liquid crystals exhibit both crystal-like and fluid-like features. In
particular, the propagation of an acoustic wave shows an unexpected occurrence
of some of the solid-like features at the hydrodynamic level, namely, the
frequency-dependent anisotropy of sound velocity and acoustic attenuation. The
non-Newtonian behavior of nematics also emerges from the frequency-dependent
viscosity coefficients. To account for these phenomena, we put forward a
viscoelastic model of nematic liquid crystals, and we extend our previous
theory to fully include the combined effects of compressibility, anisotropic
elasticity and dynamic relaxation, at any shear rate. The low-frequency limit
agrees with the compressible Ericksen-Leslie theory, while at intermediate
frequencies the model correctly captures the relaxation mechanisms underlying
finite shear and bulk elastic moduli. We show that there are only four
relaxation times allowed by the uniaxial symmetry.
