Almost most of literatures treat behaviors of asphalt binders as a homogeneous single-phase fluid, but this generalization turns out to be a serious mistake. This study introduces all the characteristic equations for asphalt binders, which are modified or unmodified. Especially, characteristic equations for a unhomogeneous multi-phase fluid for modified asphalts is first time proposed. Characteristics of each equations introduced are explained by employing dynamic shear testing data actually measured for specific asphalt binders. Differences of moving behaviors and characteristic equations between a homogeneous single-phase and a unhomogeneous multi-phase fluid are emphasized. These differences help us understand which characteristic equations must be used for a given asphalt fluid and what kinds of properties must be investigated for analysis of a specific asphalt binder. Results of this study provide how to analyse modified and unmodified asphalts, and informations necessary for binder grading.