The ohmic heating of glass furnaces by the passage of an electric current between carefully placed electrodes in the melt is a well established and growing technology in the glass industry (Scarfe 1980). Electroheat can also he generated wing an induction mi! and this is a we!! established method used by other industries. This paper examines the possibility that if the large metal susceptor is incorporated into the design of a glass furnace, then an alternating magnetic field may be used to raise its temperature and so melt the charge. One important advantage of using a susceptor coupled to an induction coil to melt glass, is that the furnace can be started up from cold. This method is therefore tailor made for applications where furnaces are not run on a continuous basis. Other advantages of electric over fuel-fired furnaces are that they are easily sealed to prevent the leakage of volatile emissions from the melt into the environment, are relatively maintenance free, and offer more control over the convection currents in the melt. A general mathematical formulation of the induction problem for a cylindrical tube in an axial magnetic field has been given by McLachlan and Meyers (1935). Their analysis has been developed further for particular application to glass furnaces. An additional problem considered here is the presence of a glass layer, which serves to protect the outer surface of the susceptor from oxidation. This layer is electrically conducting and the eddy currents generated inside it must therefore be taken into account. Maxwell's equations are taken as the starting point and it is assumed that the thickness of the susceptor is at least several times larger than the depth of penetration of the coil's magnetic field into the susceptor. The magnetic field, the current density and the power dissipation in the susceptor are calculated. Consideration is then given to the electrical characteristics of the furnace and to the problem of magnetic forces on the susceptor. The problem of the eddy current heating of a composite cylindrical system has arisen before in connection with the manufacture of thermionic valves and has received consideration from Wright (1Y37). There are, however, two important differences between that problem and the one treated here. Firstly, a complex time dependence is introduced, and this results in considerable simplification of the analysis. Secondly, the glass laycr in an induction furnace is relatively much thicker than the outer envelope in a thermionic valve, and the 'thin cylinder' approximation used by Wright cannot, therefore, be invoked.