A process for producing a clearcoat and a multi-component composition. The process comprises applying the multi-component composition to a primed substrate, an unprimed substrate, or a coated substrate. The multi-component composition comprises (A) a binder containing on average at least one isocyanate-reactive functional group, (B) an adduct prepared from (b1) a diisocyanate and (b2) a compound of the general formula I containing an isocyanate-reactive group: ##STR00001## and (C) at least one cross-linking agent containing on average at least one isocyanate group and at least one functional group which may be activated by actinic reaction.