Retardation and relaxation spectra of modified asphalt binders with nonlinear time, or in other words a stretched exponential function of time, were used for the description of accumulated compliance in the repeated creep and recovery test, as well as in transient shear flows such as startup flow. The experimental results were successfully fitted to the accumulated compliance function as well as to the stress (stress growth coefficient) in transient shear flows of several polymer-modified asphalt binders. The concept of stretched time exponential, used in this contribution, seems to be useful for the description of nonlinear behavior of modified asphalt binders and hence possibly more generally to describe other complex materials.