The invention relates to copolymers made from terpenes containing no conjugated double bonds and vinyl compounds and/or dicarboxylic acids containing one C-C double bond, and derivatives thereof, as comonomers. They are preferably prepared in a free-radical bulk polymerisation at a temperature of from 100 to 200 DEG C over the course of from 1 to 10 hours. The absence of solvents or diluents means that particularly pure copolymers are obtained. They are particularly suitable as tackifiers.