The orientation distribution function of a dumbbell undergoing rotary Brownian motion (with time constant λ) in steady shear flow and the viscosity and normal stress coefficients are computed by a perturbation expansion in small, dimensionless shear ratesλγ̇.It is found that the series expansions for both the viscosity and the first normal stress coefficient have identical radii of convergence atλγ̇=0.81.By using analytical continuation, the solution was extended toλγ̇=1.5,and compared with established results. Our results agree with earlier perturbation calculations of Kirkwood and Plock (1956), Bird and Warner (1971), and numerical calculations of Stewart and So/rensen (1972).