  A nonlinear viscoelastic theory of nematodynamic type is developed for
nematic liquid crystalline (LC) semi-flexible polymers. A measure of transient
elastic strain due to the change in length of macromolecular strands under
stress, and the director of unit length are employed in the theory as hidden
variables. In the marked contrast to the common theoretical approaches to low
molecular nematics, the effect of directors space gradient is neglected in the
present theory. Nevertheless, the theory allows describing nonlinear
anisotropic viscoelasticity and evolution equation for the director in flows of
LC polymers. When LC macromolecules are relatively rigid or when they are soft
but the flow is slow, a weakly nonlinear viscoelastic anisotropic behavior is
described by few temperature dependent parameters. In the infinitesimal case
the evolution equation for director reminds the Ericksens equation, but with an
additional relaxation term. The present theory can also be applied for
analyzing flows of concentrated polymer suspensions and nano-composites filled
with uniaxially symmetric particles.
