The Rouse-Zinun theories of polymer solution dynamics have been extended to include normal stresses as well as shear stresses and have been evaluated for low-amplitude oscillatory shear. Two normal stress coefficients (ζd characterizing a displacement function, and ζ*, characterizing the oscillation about the displacement) appear as analogs to the complex viscosity η* for shear stress. Theoretical predictions are compared with data obtained with a Weissenberg rheogoniometer on five dilute solutions of monodisperse polystyrene (M = 1.8×106 and 4.1×106) in Aroclor 1254. The models are found to describe the measured η* and ηd with equal good success, but uncertainties in η* measurements preclude complete verification. Strong evidence is presented to support the model-independent prediction that ωζd=ζ″.