The invention relates to aqueous radiation-hardenable epoxy acrylate dispersions comprising (a) an epoxy acrylate resin (P*) with at least two acrylate groups per molecule, wherein at 25 degrees Celsius, said epoxy acrylate resin is not self-disperging in water; and (b) a dispergator (D*) with at least one acrylate group per molecule, wherein said dispersions can be produced by converting, in a first step (i), in the presence of a catalyst if need be, one or several compounds (A) selected from the group of non-ionic compounds having a HLB value of less than 12, and containing at least two oxirane groups per molecule, with one or several compounds (B) selected from the group of non-ionic compounds having a HLB value in the range from 12 to 20, and which contain at least one h-acid group (ZH) per molecule. The compounds (A) and (B) are employed at an equivalence ratio EpO (A):ZH (B) in the range from 1.3:1 to 400:1, and in a second step (ii), the reactive mixture thus obtained is converted, in the presence of a catalyst if need be, with one or several non-ionic compounds having a HLB value of less than 12, and containing at least two oxirane groups per molecule (compounds A), and with one or several compounds (C) selected from the group of non-ionic compounds having a HLB value of less than 12, and which contain at least two H-acid groups. The compounds (A) and (C) are employed at an equivalence ratio EpO (A):ZH (C) in the range from 1.1:1 to 20:1. In a third step (iii), the reactive mixture thus obtained is converted, in the presence of a catalyst if need be, with acrylic acid by ring opening of all epoxy groups. In a fourth step (iv), the reactive mixture thus obtained is disperged in water.