The Rouse–Zimm 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 × 105) in Aroclor 1254. The models are found to describe the measured η* and ζd with equal good success, but uncertainties in ζ* measurements preclude complete verification. Strong evidence is presented to support the model-independent prediction that ωζd = η″.