A. I. Leonova and V. S. Volkovb UDC 532.584+612.117 A weakly nonlinear viscoelastic theory is developed for nematic liquid crystalline (LC) polymers. A small transient elastic strain due to the change in length of macromolecular strands under stress and a director of unit length are employed in the theory as hidden variables. The theory allows describing anisotropic viscoelasticity and the evolution equation for the director in flows of relatively rigid LC polymers or in slow flows of LC polymers with flexible spacers. As shown, omitting the director gradient does not affect macroscopic predictions of the theory. In the infinitesimal case, the evolution equation for the director looks like the Ericksen equation, but with an additional relaxation term. Although the present theory is mostly applicable for thermotropic LC polymers it can also be used for concentrated lyotropic LC systems, as well as for analyzing flows of concentrated polymer suspensions and nano-composites filled with uniaxially symmetric particles. aThe University of Akron, Akron, Ohio 44325-0301, USA; email: leonov@uakron.edu; bInstitute of Petrochemical Synthesis, Russian Academy of Sciences, 29 Leninsky Ave., Moscow, 117912, Russia; email: vsvolk@ips.ac.ru. Published in Inzhenerno-Fizicheskii Zhurnal, Vol. 76, No. 3, pp. 31-38, May-June, 2003. Original article submitted November 12, 2002.