Process for the preparation of ethylene copolymers, and their use as additives to mineral oil and mineral oil distillates. The invention relates to a process for the preparation of terpolymers of ethylene and at least 2 further olefinically unsaturated compounds by polymerization in a tubular reactor fitted with at least one side branch, wherein the fresh monomer components, which are introduced into the tubular reactor via the reactor inlet (the primary stream) or via the side branch or side branches (secondary stream or secondary streams), in each of the streams contain ethylene and at most one further olefinically unsaturated compound.