Coating materials curable thermally and with actinic radiation, comprising (A) at least one binder containing isocyanate-reactive functional groups and (B) a crosslinking component comprising (i) free and/or blocked isocyanate groups, (ii) reactive functional groups containing at least one bond which can be activated with actinic radiation, (iii) flexibilizing segments which as part of three-dimensional networks lower their glass transition temperature Tg, and (iv) hardening segments which as part of three-dimensional networks raise their glass transition temperature Tg; with the proviso that the crosslinking component (B) comprises or consists of at least one constituent which has the features (i) and (ii); processes for their preparation, and their use.