Abstract: Copolymers crosslinkable by a free radical method and having a number average molecular weight of from 1500 to 6000 and a molecular weight distribution corresponding to a polydispersity of from 1 to 4.0 are obtainable by polymer-analogous reaction ofA) a copolymer (A) which is composed ofa1) from 50 to 85 mol % of a monomer (a1) containing the structural element of methacrylic acid anda2) from 15 to 50 mol % of another monomer (a2) undergoing free radical polymerization,a3) from 5 to 50 mol % of the total amount of the monomers (a1) and (a2) being monomers (a3) which carry functional groups and whose functional groups are capable of undergoing a condensation or addition reaction,and is obtainable by free radical mass or solution polymerization at from 140.degree. to 210.degree. C. and with an average residence time of from 2 to 90 minuteswithB) an olefinically unsaturated monomer (B) which carries a functional group which is complementary to the functional groups of the monomers (a3).