A process for the production of a multi-layer coating, wherein a primer layer which is electrically conductive in the at least partially cured state is applied by electrodeposition from an electrodeposition coating agent (I) to an electrically conductive three-dimensional object, at least partially cured exclusively by the action of near infra-red radiation substantially only on the surfaces of the object exposed to the radiation, and an additional coating layer is applied by electrodeposition from an electrodeposition coating agent (II) which is different from electrodeposition coating agent (I), and then this additional coating layer as well as completely uncured or incompletely cured area parts of the primer layer produced from electrodeposition coating agent (I) are cured.