  The quasi--equilibrium approximation is employed as a systematic tool for
solving the problem of deriving constitutive equations from kinetic models of
liquid--crystalline polymers. It is demonstrated how kinetic models of
liquid--crystalline polymers can be approximated in a systematic way, how
canonical distribution functions can be derived from the maximum entropy
principle and how constitutive equations are derived therefrom. The numerical
implementation of the constitutive equations based on the intrinsic dual
structure of the quasi--equilibrium manifold thus derived is developed and
illustrated for particular examples. Finally, a measure of the accuracy of the
quasi--equilibrium approximation is proposed that can be implemented into the
numerical integration of the constitutive equation.
