Disclosed are a thermoplastic polymer-linked-asphalt composition and a process for making a thermoplastic polymer-linked-asphalt. More particularly, the present invention relates to the reaction and resultant linking of a combination of epoxide-containing polymers and anhydride-containing polymers to asphalt to form a polymer-linked-asphalt composition having higher softening points. The improved polymer-linked-asphalt product is particularly useful in roofing applications.