The dynamics of rodlike polymer molecules in the nematic phase are mainly controlled by the rotational diffusivity, D-r which is highly sensitive to molecular weight. However, few experimental determinations of D-r for polymer solutions at concentrations in the nematic phase have been made. We invoke Doi's theory of liquid crystalline polymer rheology to extract D-r from experimental measurements of the transverse Miesowicz viscosity, eta(c), of nematic solutions. Transverse Miesowicz viscosities were measured for a series of poly(n-hexyl isocyanate) (PHIC) polymers at fixed dimensionless concentration (c/c* = 1.25) in p-xylene, by orienting the director with a high de electric field. The rotational diffusivity of PHIC was found to be independent of shear rate and proportional to M-w(-4.95 +/-0.29). This scaling is in excellent agreement with Doi's molecular theory, which predicts that Dr scales as M-5 at fixed c/c*. The experimental values of D, were compared with theoretical values calculated a priori from molecular dimensions and the solution concentration. The numerical constant which multiplies Doi's predicted Dr was found to be of order 10(1) for the nematic PHIC solutions, in contrast with values of order 10(3) reported for semidilute solutions of rodlike molecules.