The response times of liquid crystal display devices are determined by a range of factors but the most important of these is usually the rotational viscosity coefficient, gamma(1). In order to understand the relationship between molecular structure and viscosity it is of considerable interest to measure this viscosity coefficient for a variety of nematogens. Here we report the determination of gamma(1) for 4-octyl-4'-cyanobiphenyl-d(2) at two temperatures using deuterium NMR spectroscopy. In these experiments the time taken for the alignment of the director can be changed by a field, either magnetic or electric. To do this the liquid crystal film was enclosed in a cell which allows the application of an electric field within the NMR spectrometer. The rate of director relaxation was followed by recording the deuterium NMR spectrum as a function of time during the process of turning the electric field on or off. We have carried out the experiments for a geometry in which the director orientation with respect to the magnetic field of the spectrometer does not exceed 45degrees. The alignment of the director throughout the relaxation process was observed to be uniform. The director relaxation was found to follow closely the predictions of the torque-balance equation given by the Leslie-Eriksen theory. The relaxation times for the turn-on and turn-off processes were determined from this equation and found to be of the order of 1-2 ms. A knowledge of the anisotropic electric and magnetic susceptibilities then allows the determination of the rotational viscosity coefficient.