An electrical multilayer component comprising a sintered monolithic body and a method for the manufacture of the component.The sintered monolithic ceramic body of the electrical multilayer component includes cavities which alternate between layers, and are open toward end faces which are on opposite sides. The cavities also open toward lateral surfaces of the ceramic body over their entire lengths. The cavities contain ceramic particles which are distributed therethrough to act as supporting elements and are completely filled with a metal or metal alloy whose melting temperature is considerably lower than the sintering temperature of the ceramic body. The metal or alloy has the property of wetting the surfaces of the ceramic layers in the cavities in the molten condition. Contact elements are then applied to the end faces, the contact elements being impervious to the metal melt. Spaces free of metal are present in the cavities at the lateral surfaces of the ceramic body.