A process for the preparation of block copolymers by polymerising at least one further monomer (B) onto the reactive terminal groups (a2) of existing polymer chains (A), these groups having been produced by supply of energy, in which the reactive terminal groups (a2) are produced, by irradiation with actinic light having a wavelength lambda of from 230 to 450 nm, from terminal groups (a1) which represent photopolymerisation initiators bonded to the polymer chains (A).
