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This paper presents a new method for accurately determining all possible steady-state operating points of a switch-mode contactless power transfer (CPT) system. The method is based on a stroboscopic mapping model and accurate calculation of its fixed points corresponding to circuit zero current switching (ZCS) conditions. Four steady-state operating points are identified for, e.g., inductor-capacitor-inductor ( LCL)-type CPT system. Voltage and current waveforms and switching periods are determined. Parameter influences on ZCS periods are studied by bifurcation diagrams. Both PSpice simulation and experimental results have verified the proposed method. The results provide new opportunities for a practical CPT system to operate at different soft switching frequencies. The method is very useful for analyzing switch-mode resonant circuits and designing new power flow controllers.