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The Dynamic Ergodic Divertor (DED) of the TEXTOR 94 tokamak will work at the regimes of DC current and AC current at frequencies up to 10 kHz. In order to design the mechanical structures supporting the DED coils and the graphite protective tiles it is necessary to take into account the induced eddy currents, especially at high frequencies. The temperature rise and mechanical forces in the structures should be within acceptable limits. The screening effect of the DED coils in the plasma region should be minimized. The modeling of the DED electromagnetic field is discussed. The problem is solved numerically with the ANSYS code. For comparison, some simplified technique is employed. Two approaches are used for the different types of structures: thin shell approach and infinitely thin skin-layer approach. The eddy currents and energy losses in the structures have been defined. The 2-D and 3-D nonstationary thermal problems have been solved and the temperature rise in the structures has been calculated for the steady state regimes. The evaluation of the static and cyclic strength of the structures has been made. Based on parametric studies, the parameters of the coil and tile supporting structures have been optimized.