Asphalt concrete exhibits creep and relaxation behaviors. Its magnitude normally depends strongly on temperature, stress level and loading duration. Attempts to predict the crack initiation and propagation in fracture of asphalt concrete are complicated by all such variables. Pseudo strain concept in the correspondence principle has been extended to nonlinear viscoelastic behavior of asphalt mixtures by introducing a nonlinear reference modulus. It has been demonstrated that dissipated pseudo strain energy is a damage parameter. It can be successfully used to quantify the fatigue microdamage and tertiary microdamage of permanent deformation. The significant recovery of pseudo stiffness after introducing rest periods indicates the healing effect due to rest periods. Modified Paris' law in which the J-integral rather than stress intensity factor is used is applied to quantify the microdamage initiation during fatigue and permanent deformation tests.