The change of the viscosity along capillary and slit dies for flow of nematic liquid‐crystalline polymeric melts is examined. The pressure profile as measured along a slit die equipped with an array of nine pressure transducers is compared with calculations that are based on three models: (I) viscosity changing downstream because of the reduction of the initial orientation in the liquid‐crystalline melt, (II) accounting for the flow development region, based on the fluid behavior during start‐up of flow, and (III) pressure dependent viscosity. It is found that the nonlinearity of the pressure profile in the slit can be best explained by the effect that the pressure has on the viscosity. Bagley plots from capillary measurements, however, do not distinguish between the causes of their concavity. Model III alone can not fully account for the nonlinearities of this plot.