A hydrophilic or hydrophobic polyurethane containing on average per molecule at least one olefinically unsaturated structural unit selected from the group consisting of pendant, internal, and terminal, acyclic and cyclic terpene units; graft copolymers of the polyurethane with olefinically unsaturated monomers, processes for preparing the polyurethane and the graft copolymers, and their use for preparing coating materials, adhesives, and sealing compounds.