An understanding of the flow behavior of liquid crystalline polymers (LCP's) is of immense practical value because of the potential to form high modulus materials from these polymers. These fluids exhibit a high degree of structure even in the quiescent state, as evidenced by their ability to transmit polarized light. In an effort to understand how the structure changes during flow, we have carried out a study on the transient shear flow properties of two thermotropic copolyesters of 60_ and 80_mole % para_hydroxybenzoic acid (PHB) and polyethyleneterephthalate (PET) and a lyotropic system of poly_p_phenyleneterephthalamide (PPT) in 100% sulfuric acid. In one of the first theories concerned with the flow behavior of liquid crystalline fluids, which was proposed by Ericksen, the transient flow properties are all predicted to be due to changes in orientation of a director which describes the orientation of packets of rod_like molecules. Stress growth, interrupted stress growth, and stress relaxation experiments are carried out on the three LCP's and at first sight are in qualitative agreement with the predictions of Ericksen's theory. However, wide angle X_ray scattering analysis of quenched samples subjected to shear flow along with annealing experiments on oriented samples indicate that these materials do not orient readily in shear flow. Furthermore, orientation generated during extensional flow relaxes at a rate much faster than is indicated by the interrupted stress growth experiments. It is concluded that the stress growth response of LCP's is due to a disruption of a domain structure which exists within the fluid rather than to orientation changes of the domains of rod_like molecules.