The invention relates to olefinically unsaturated polyisocyanates containing allophanate groups and having an NCO content of 6 to 20% by weight, an iodine value of 15 to 150, a content of hydrocarbon chains containing 12 to 30 carbon atoms of 100 to 700 mg/g and a content of allophanate groups of 10 to 300 mg/g, to a process for their production by reaction of a polyisocyanate component containing urethane groups with excess polyisocyanates, and to a one-component coating composition containing these olefinically unsaturated polyisocyanates as binders.