The invention describes a method and an apparatus for the rapid melting of in particular high-purity, aggressive and/or high-melting glasses in a skull crucible, in which high-frequency energy is introduced into the contents of the crucible by means of a coil arrangement surrounding the skull crucible, in order to heat the melt, and the batch is laid and the molten glass discharged in the upper region of the crucible, and undissolved constituents of the batch are retained by means of a cooled bridge which is immersed in the melt. According to the invention, the glass is taken off above the coil arrangement (1.3) and is fed for further processing without flowing through the coil region. This has the advantage that simple, conventional components can be used to connect the melting unit to the further-processing stations, and the type of connection can be selected in such a way that it is possible to prevent the quality of the glass from being impaired by connection techniques which are less than optimum.