The invention relates to radically copolymerizable acetophenone or benzophenone derivatives, obtained by reaction of a) (meth)acrylic compounds exhibiting at least one isocyanate-reactive group [compounds a)] with b) compounds exhibiting at least two isocyanate groups [compounds b)] and c) acetophenone or benzophenone derivatives exhibiting at least one isocyanate-reactive group [compounds c)]. The invention also relates to copolymers that contain copolymerizable photoinitiators of the invention and to the use of said copolymers in UV-crosslinkable compositions, particularly hot-melt adhesives.