Abstract: The invention relates to a process for the modification of an olefin polymer to form a coupling agent by grafting it with an unsaturated acid or acid derivative in the presence of a free-radical initiator. The process comprises stages at whicha) the olefin polymer, the unsaturated acid or acid derivative and a first free-radical initiator are heated together to a temperature at which the first free-radical initiator substantially breaks down into free radicals, andb) the reaction mixture derived from stage a) is heated together with a second free-radical initiator to a temperature at which the second free-radical initiator substantially breaks down into free radicals. By the process, olefin polymers can be modified effectively without their macromolecules degrading excessively.