Abstract
The hydrodynamic theory of the smectic and the nematic phase is generalized to the vicinity of the nematic-smectic-A phase transition by including the motion of the three slowly relaxing quantities. The sound spectrum is recalculated and found to be in agreement with recent experimental data on the dispersion and damping of first sound. In addition, the theory predicts two interesting effects for the nematic phase: (i) a smectic layer ordering induced by a stationary shear flow, and (ii) the existence of high-frequency shear waves.