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The phenomenon of hysteresis occurring in a series nonlinear resonant circuit has interested engineers for a long time. The phenomenon is associated in literature with a resonance occurring at a critical value of applied voltage where the nonlinear inductance, variable with the magnitude of the forcing function, reaches a value so as to resonate with the fixed capacitor. This is probably the reason for using the term ferroresonance to describe the hysteresis behavior. The validity of such an explanation fails when circuits with reactors of sharp magnetic saturation, such as Deltamax and Orthonol, are considered. The inductance of such reactors may be approximated without appreciable error by linear regions of zero and infinite inductances. As will be shown in this paper, the hysteresis phenomenon still exists and even becomes more prominent as the magnetic saturation becomes sharper. On the other hand, the usual explanation given in literature fails when applied to such ideal circuits, since an inductance having values of either zero or infinity could not resonate with a finite capacitance.