An electroslag remelting and surfacing apparatus having a cooled mould comprising a plurality of superimposed sleeves which are electrically insulated from one another. The top sleeve of the mould, being substantially a non-consumable electrode, has a current lead and a lining of electrically conducting material. If provided with a radial electrically insulating layer, it may also serve as a single-coil inductor adapted to impart a rotary motion to the slag pool.