Mixtures curable thermally and with actinic radiation and containing carbamate and/or allophanate groups, comprising (A) at least one of (A1) low molecular mass compounds, oligomers and polymers containing allophanate groups, carbamate groups, and carbamate and allophanate groups, and (A2) low molecular mass compounds, oligomers and polymers containing allophanate groups, carbamate groups, and carbamate and allophanate groups, and additionally allophanate- and/or carbamate-reactive functional groups, which are substantially or entirely free from reactive functional groups which contain at least one bond which can be activated with actinic radiation, and (C) at least one constituent containing on average per molecule at least one reactive functional group having at least one bond which can be activated with actinic radiation; with the proviso that if only (A1) is used, the mixtures further comprise (B) at least one of low molecular mass compounds, oligomers and polymers containing allophanate- and/or carbamate-reactive functional groups.