Abstract The viscosity functions of several polymer‐modified asphalts (PMAs) were studied at different temperatures in steady‐state rate sweep tests. The materials were obtained by mixing different base asphalts with either styrene‐butadiene‐styrene (SBS), ethylene‐vinylacetate (EVA) or reactive ethylene terpolymers (RET). The first two polymers form a physical network that is swollen by the asphalt, while the latter is functionalized with glycidylmethacrylate (GMA) and can crosslink and/or chemically bond with the molecules of asphaltenes. In the presence of SBS or EVA, at certain temperatures, the viscosity curves exhibit a Newtonian behavior at low shear rates, followed by two distinct shear‐thinning phenomena. In some cases, the first shear‐thinning is preceded by a small shear‐thickening region. Similar phenomena are not present in the viscosity curves of the RET‐modified asphalts and can be related to a temporary nature of the physical polymer network. Polym. Eng. Sci. 44:2185–2193, 2004. © 2004 Society of Plastics Engineers.