The invention relates to a method and coating agents used in the method
which provide good adherence to and good corrosion protection of metal
substrates; the coating coating agents are cross-linkable via radical
polymerization. Adhesion promoting compounds are present in the
conversion layer in a quantity of about 0.01 to 40 weight percent and
contain, on average, one reactive unsaturated group and at least one
H-active group per molecule.