Aqueous electrophoretic lacquer capable of being deposited cataphoretically, containing A) an aqueous dispersion of cationically modified polyurethane (meth)acrylates (a1) with terminal, ethylenically unsaturated (meth)acrylic double bonds, and reactive thinner (a2) with at least two ethylenically unsaturated (meth)acrylic double bonds, the (meth)acrylic double bonds of the mixture of (a1) and (a2) corresponding to a bromine number of 20 to 150 g bromine/100 g solids, and B) photoinitiators and optionally free-radical initiators capable of thermal activation, the terminal, ethylenically unsaturated (meth)acrylic double bonds of the polyurethane (meth)acrylates being bonded with the anionically modified polyurethane prepolymer via urethane, urea, amide or ester groups, and optionally conventional auxiliary substances and additives, pigments and/or fillers.