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This contribution deals with the stability analysis of the alternating current arc furnace dynamic operation connected to a supply system using bifurcations theory. The analysis is carried-out in the time domain through the computation of the system eigenvalues and a careful study of the bifurcation diagrams and stability at the equilibrium points. The effect of the bifurcation parameter variation on the arc furnace dynamic behavior is analyzed. The method allows an appropriate assessment of nonlinear oscillations produced by of alternating current Electric Arc Furnace.