The invention relates to an electrically conductive, weldable, anti-corrosion composition that is substantially devoid of solvents, for coating metal surfaces. Said composition contains the following, (in relation to the total composition): a) between 5 and 98 wt. % of an organic binding agent; b) between 0 and 15 wt. % of an anti-corrosion pigment, c) between 20 and 90 wt. % of a conductivity pigment with a density of at least 3 g/cm and/or between 2 and 20 wt. % of a conductivity pigment with a density of less than 3 g/cm . The viscosity of said composition permits it to be applied in a coil-coating method. Preferably, the percentage by weight of said conductivity pigment increases as the density of the pigment increases. The binding agent can be cured by the action of high-energy radiation and preferably contains the following components: aa) at least one polyester resin, urethane resin or epoxy-modified (meth)acrylate resin; ab) at least one reactive thinner; and ac) at least one photoinitiator. According to said method for applying this type of anti-corrosion composition, in a preliminary step, the metal surface is brought into contact with a liquid that contains at least one low-molecular organic compound with at least one group that can be cross-linked by a radical polymerisation and at least one H-active group. The invention also relates to correspondingly coated sheet metal and metal parts, which can be subsequently painted, and to a method for producing painted metal parts of this type.