Steady measurements in capillary and slit dies and transient experiments in a cone-plate system are presented for two thermotropic copolyesters, X7G (R) and Vectra A950, and a thermotropic copolyesteramide, Vectra B950. The wide shear rate range covered, from 10(-2) to 10(4) s(-1), allows us to observe the three regions defined by Onogi and Asada (1). However, the copolyesters on one hand, and the copolyesteramide on the other, show different theological behavior that can be summarized as follows : For X7G (R) and Vectra A950 : i. higher viscosities in slit than in capillary die flow; ii. upward-concave pressure profiles in slit die flow; iii. overshoot peaks in transient experiments at a shear strain gamma(M) = 2. For Vectra B950 : i. lower viscosities in slit than in capillary die flows; ii. linear or slightly convex pressure profiles in slit die flow; iii. overshoot peaks in transient experiments at a shear strain of gamma(M) = 180. These seemingly contradictory results are explained by the competition between the texture changes along the flow (a transition from a worm texture to a flow-aligned region) and the pressure effect on viscosity.