The origin of the nonlinearity observed in Bagley plots of thermotropic copolyesters has been investigated experimentally. With the aid of a two‐piston slit rheometer the dependence of the viscosity on the hydrostatic pressure has been determined directly. This dependence only accounts for part of the nonlinearity of the Bagley plots. Using slit dies with either a convergent or a divergent entrance, concave as well as convex pressure profiles are obtained. This can only be explained by a change in the molecular orientation induced by the flow in the entrance zone. The presence of wall effects has been evaluated by measuring the pressure profiles in slits of different heights; it does not explain the nonlinearity of the Bagley plots. The origin of the nonlinearity of Bagley plots must be due to both pressure and molecular reorientation effects. The nature and importance of these reorientation effects are shown to depend on the entrance geometry.