In this work we attempt to determine the origin of damped stress oscillations upon flow start-up of a nematic liquid crystalline monodomain. These damped stress oscillations were first observed by Gu et al. (1993) in the cone-plate flow cell and have since also been observed by Mather et al. (1997) in the parallel disk cell. Although Mather's work explained the cause of the stress oscillation damping in the torsional flow cell, the origin of the damping in the cone-plate device remains a mystery. Here we report finding similar damped stress oscillations in the cylindrical Couette cell and combined with the optical experiments reported earlier by Cladis and Torza (1975, 1976) we are able to propose an explanation for the damping in this geometry. We also report new optical experiments using the cone-plate cell in hopes of determining a cause to the damping in the cone-plate cell.