A control device of an electric arc furnace that controls, in a melting phase and subsequently in a flat bath phase, an energy supply device with first control values (A1), such that the energy supply device supplies electrical energy to electrodes of the electric arc furnace via a furnace transformer. The control device, in both phases, further controls a positioning device with second control values (A2), such that said positioning device positions the electrodes relative to the unmolten steel-containing material in the melting phase and relative to the molten steel in the flat bath phase. As a result, electric arcs are formed in both phases, by means of which the steel-containing material is melted or the molten steel is further heated.