Four kinds of modified asphalts and one kind of base asphalt were selected to conduct repeated creep tests over a wider stress range at high temperatures. Non recoverable compliance Junr was computed at different temperatures and stress levels to analyze the change rule from linear to nonlinear viscoelastic responses of modified asphalts, and then the Junr values within the nonlinear response regions of asphalt binders at a typical high temperature of asphalt pavement in summer were chosen to make a correlation analysis with the results from rutting tests of asphalt mixtures. The results show that the linear region of asphalt binders significantly becomes narrow with the rise of temperatures, and the Junr values begin to dramatically increase after entering the nonlinear response regions, demonstrating that their resistance to permanent deformation markedly reduces. The high temperature properties of modified asphalts at different temperatures and stress levels are diverse, and the high temperature property of high strength modified asphalt is the best at higher temperature and stress level. Under limited sample situations, the Junr values of asphalt binders in the nonlinear response regions have good correlation with the results from rutting tests of asphalt mixtures, and it indicates that permanent deformation of asphalt mixtures is in close relation with nonlinear viscoelastic responses of asphalt binders.