Nonlinear oscillations in power systems involving the excitation of nonlinear inductance with a linear capacitance in series have been termed ferroresonant oscillations. Such oscillations are unpredictable and their occurrence is of serious concern predominantly because of possible damage to equipment such as transformers. The probability of system disruption due to the occurrence of ferroresonance has increased with improvements in the characteristics of transformer steel and the use of higher and higher voltages for transmission of bulk power. Conditions that lead to the occurrence of ferroresonant oscillation, given a system, therefore, need to be known. It will be shown that for any disturbance the autonomous form of the nonlinear differential equation representing the system with two-degrees of freedom decays to a point attractor; that is, it is always stable.