A process for coating electrically conductive substrates by (1) applying an electrocoat film to an electrically conductive substrate and curing it to give an electrocoat and then (2) applying a layer of a pulverulent coating material to the electrocoat and curing it to give a powder coat or alternatively (1) applying an electrocoat film to an electrically conductive substrate and drying it without fully curing it, (2) applying a layer of a pulverulent coating material to the dried electrocoat film(s) and (3) jointly curing the dried electrocoat film and the layer of the pulverulent coating material to give the electrocoat and the powder coat wherein the pulverulent coating material comprises (A) at least one epoxy resin having a melting point, melting range or glass transition temperature>30° C., (B) at least one carboxyl-containing polyester resin having a melting point, melting range or glass transition temperature>30° C., and (C) at least one polycarboxylic acid having a melting point of between 80 and 160° C.