Analyses of the self-saturating magnetic amplifiers are generally restricted to the pure resistive load cases. There are a few reports related to capacitive loads and some others on inductive loads. The possibility of occurrence of abnormal phenomena in the self-saturating magnetic amplifier with capacitive load has been reported, but their mechanism of circuit behavior is not yet clear. In this paper, the circuit operation is analyzed in detail from the stability point of view and the mechanism of peculiar modes is investigated. The circuit operation is represented by the nonlinear difference equations which are derived from the continuity of both charge and flux linkage. Linear difference equations for small disturbances occurring at the equilibrium state directly suggest the stability of the equilibrium state and possibility of occurrences of the peculiar modes. Further, the control characteristics and the transient responses are calculated and the criteria for prevention of the peculiar modes are found in simple forms. The theoretical analyses show good agreement with experimental results.