Asphalt‐modification was studied using two different types of triblock copolymers both with star‐like molecular architecture: poly(styrene‐b‐butadiene‐b‐styrene), SBS, and poly(styrene‐b[(butadiene)1−x‐(ethylene‐co‐butylene)x]‐b‐styrene), SBEBS, to elucidate the effect of the molecular characteristics of the polymer and the polymer‐content on the morphology and rheological behavior of polymer‐modified asphalt, P‐MA. The P‐MAs were prepared using a hot mixing process and characterized using fluorescence microscopy and oscillatory shear flow measurements under linear viscoelastic conditions. Results revealed that the morphology of the polymer‐rich phase and rheological behavior of the P‐MA are dependent on the type and concentration of polymer: (i) P‐MAs prepared with SBEBS exhibited higher dispersion in the asphalt matrix and were more elastic and less responsive toward frequency changes; (ii) P‐MAs prepared with the polymer (SBS or SBEBS) of the larger molecular weight displayed higher elasticity; and (iii) the increase in the polymer concentration from 3 to 10 wt% resulted in the creation of P‐MAs with higher elastic response. These results substantiate the importance of the molecular characteristics of the polymer in determining the properties of P‐MAs, in particular composition of the elastomeric‐b and molecular weight of these polymers, and the results are explained considering the molecular characteristics of these polymers and the polymer/asphalt interaction. POLYM. ENG. SCI., 53:2454–2464, 2013. © 2013 Society of Plastics Engineers