A light-emitting semiconductor device has (a) a semiconductor body (1) with a layer sequence (7) capable of emitting electromagnetic radiation of a first wavelength range in the UV, blue and/or green region; and (b) a luminescence conversion element which converts radiation of the first wavelength range to radiation of one or more second, different wavelength ranges so that the device emits mixed radiation in the first and second wavelength ranges. Preferably, the luminescence conversion element consists of organic dye molecules in a plastic matrix preferably of silicone, thermoplastic or thermosetting material, especially an epoxide resin or polymethyl methacrylate matrix, and/or an inorganic phosphor (preferably a Ce-doped garnet, especially Ce:YAG) in an epoxide resin or low melting point inorganic glass matrix.