A reactive paint to be completely cured in air with binders that bear ethylenically-unsaturated groups, that can be cured by radical polymerization either thermally or both thermally and by UV light or high-energy radiation in a dual-cure method. The paint contains a combined initiator system consisting of thermal initiators and UV initiators and reactive oligomers that are formed from addition compounds of a reactant of formula (4) and a reactant of formula (5) In this formula, X=—CO—CH═CH2 or —CnHm or —CO—CnHm. —CnHm is an aliphatic residue with 1 to 3 C atoms, whereby 0, 1, 2 or 3 X substituents are formed by —CnHm, and Y is a hydrocarbon chain of 3 to 8 atoms that can also contain heteroatoms. Also provided is a method for curing by radical polymerization. The polymerization is first started thermally under air and then is continued either thermally or photoinitiated under air or protective gas, and a use in paint systems, especially in automobile manufacturing or as a binder.