Studies on the melting in a single-screw extruder have mainly concentrated on the Maddock melting mechanism. The dispersive melting mechanism, named by us, is of great practical utility. A six-block physical model is first proposed for the dispersive melting mechanism in the present study. Then nonisothermal non-Newtonian mathematical models for the dispersive and Maddock melting mechanisms are developed. It has been demonstrated that the dispersive melting model has a number of advantages over the Maddock melting model: the mechanical power consumption can be decreased; the polymer temperature profile is more uniform and its average temperature is lower. Furthermore, melting can be accelerated and hence the total melting length shortened.