This paper focuses on anomalous nonlinear phenomena in a thyristor controlled reactor-static var compensator (TCR-SVC) system, called switching time bifurcation, and clarifies the relationship between the occurrence of nonlinear phenomenon and the intrinsic characteristics of the circuit equation with switching function. The occurrence of nonlinear phenomenon in a TCR-SVC system cannot be predicted when the dynamics of the circuit related to the switching action is neglected. Therefore, this paper considers the dynamics related to the switching operations in the analysis of nonlinear phenomena. The parametric excitation of circuit is discussed in relation to the homogeneous expression of the circuit equation. This paper indicates that the homogeneous equation of the TCR-SVC system results in Hill's equation, and it can be approximated as Mathieu's equation. The occurrence of nonlinear phenomena in the system is evaluated using the characteristics of Mathieu's equation. The anomalous nonlinear phenomena occur when the natural frequency of Mathieu's equation coincides with the frequency of the ac voltage in a TCR-SVC system. The parametric excitation is also confirmed through the characteristics of Hill's equation. This study clarified the interaction between the switching dynamics of the circuit and its external excitation, and clued the occurrence of nonlinear phenomena in the circuit. The proposed procedure can also be applied to the analysis for other switching converter circuits with periodic excitation source.