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We report an experimental and modeling analysis of ferroresonance phenomena in a series inductance-capacitance-resistance circuit with a saturable inductor. The nonlinear reactor core is made of a nanocrystalline ribbon whose magnetic properties can be modified by suitable thermal treatments. This choice of core allows us to investigate the influence of the magnetization curve on the evolution of the ferroresonance phenomenon. We detected different ferroresonance modes experimentally and reproduced them by simulation. We gave particular attention to the longitudinally field-annealed alloy, whose magnetization characteristic is close to a step ideal curve; this feature enables us to analytically interpret the ferroresonance mechanism and predict the conditions that lead to a stated evolution of the phenomenon.