Abstract: A method of welding workpieces of high-temperature superalloys is provided. Welding filler is applied in a plurality of layers to a surface of the workpiece via a heat input zone and a supply zone for supplying the welding filler into the heat input zone. The heat input zone and the supply zone on the one hand and the workpiece surface on the other hand are moved in relation to one another. A polycrystalline weld seam is generated by remelting a previously applied layer of the plurality of layers. Welding parameters are chosen such that a cooling rate during a solidifying of the material is at least 8000 Kelvins per second. Further, a welding apparatus for carrying out such a method is provided.