Development of normal stress in the direction perpendicular to the plane of shear is an important feature of the nonlinear viscoelastic behavior of asphalt binders. Here, we study the significance of this phenomenon with the help of stress-relaxation experiments in torsion. We conducted these experiments using a dynamic shear rheometer on an unmodified binder and polymer modified binder, at different temperatures and aging conditions. The results not only illustrate the nonlinearity of the behavior but also show certain distinctive characteristics of the relaxation behavior (torque relax faster than normal force) and it is seen that new constitutive models are required to predict such behavior. © 2012 Elsevier Ltd. All rights reserved.