The start-up, reversal, and cessation of capillary Poiseuille flows of uniaxial isothermal incompressible discotic nematic liquid crystals are characterized using analytical, computational, and scaling methods, for low (linear regime) and high (nonlinear regime) pressure drops. In the linear regime, transient flows provide information on the main viscoelastic material properties, including the steady shear Miesowicz' viscosity, the transient reorientation viscosity, as well as the viscosity reduction due to backflow. It is shown that cessation of weak flow provides a way to measure pressure drops. Transient flows in the nonlinear regime involve orientation-dependent material functions. The flow rate in start-up is characterized by an overshoot and strain scaling, similar to stress overshoot in simple shear. Recoil after cessation of flow is shown to be a direct function of stored Frank elastic energy. Scaling and computation show that the maximum recoil volume is shown to be close to R-3, where R is the capillary radius. Scaling and computation show that flow reversal under large pressure drops is characterized by the formation of a sharp cusp at a time equal to the orientation time scale of the material. (C) 2003 The Society of Rheology.