The rheological properties of polymeric liquid crystals are quite complicated and theories over the last decade and a half have made great progress in explaining this seemingly unique behavior. Most theories have considered only the elastic stress and neglected the viscous stress which can be measured by determining the amount of stress instantaneously lost on cessation of shear. The elastic stress is the stress that is left which subsequently decays with time after cessation. Data is presented that shows the viscous stress contribution determined from shear cessation experiments is present for both the biphasic and liquid-crystalline mesophase of hydroxypropylcellulose-water solutions. This system shows the three regions for the shear viscosity at higher concentrations. The viscous stress is the dominant contribution at high shear rates, well within region III, and is caused by viscous drag on the molecules. The viscous stress contribution is still present in the intermediate region II although to a lesser extent (approximately 20% of the total); however, as region I is approached it becomes more prominent. We explain this behavior as due to a phenomenon similar to superplasticity by viscous dissipation between domains or within defects.