  This paper is concerned with the incompressible limit of the compressible
hydrodynamic flow of liquid crystals with periodic boundary conditions in R^N(N
= 2, 3). It is rigorously shown that the local (and global) strong solution of
the compressible system converges to the local (and global) strong solution of
the incompressible system. Furthermore, the convergence rates are also obtained
in some sense.
