A study of the rheology and orientation behavior of a thermotropic copolyester of 73 mol% hydroxybenzoic acid and 27 mol% hydroxynaphthoic acid is carried out using capillary dies of different aspect ratios. The dramatic effect of the orientability associated with flow in convergence is demonstrated. The long relaxation time of the polymer preserves the orientation developed in the flow field, which is correlated with observed viscosity and extrudate swell behavior. The nonlinearity in Bagley plots of TLCP is shown to be related to the changes in the morphology that exist with changing die length. The behavior of TLCP extrudate swell and shrinkage is interpreted with reference to the deformation history. Extrudate swell is positive for short length dies, where the oriented morphology developed in the converging section is not fully relaxed. For longer length dies, where shear flow history predominates, negative die swell is observed. Both a strong reduction in the die swell and a change in shear rate sensitivity in the region of L/D 2.5 and 5 are explained by the delayed attainment of a shear flow velocity profile.