In an inductively coupled power transfer (ICPT) system, a primary capacitance is usually used to minimize the VA rating of power supply, and a secondary capacitance is adopted to maximize the power transfer. The changes of the secondary capacitance because of environmental temperature or other factors will alter the resonant frequency of the secondary side, and thus the power transfer capability is varied. In this study, the power transfer capability of ICPT systems is investigated in detail when the secondary capacitance changes. A resonant frequency control strategy is suggested to keep the system operation frequency to follow closely the secondary resonant frequency when the secondary capacitance varies. This new strategy is based on the synergic action of the system operation frequency and the primary capacitance. The performance of three frequency control methods, that is the resonant frequency control, the traditional variable frequency control, and the fixed frequency control, are compared when the secondary capacitance varies. A distinguish feature of a resonant frequency control is that the power transfer is an approximately linear function of the secondary capacitance. This linear characteristics facilitate a voltage control strategy being used to keep the load power unchanging when the secondary capacitance varies. A traditional viewpoint in an ICPT system is that maximizing of output power is achieved when the system operation frequency is equal to the secondary resonant frequency. Numerical simulations show that the power output by a resonant frequency control do not always dominate the power output from other two frequency control methods. This phenomenon suggests that above traditional viewpoint is a misconception, and should be reexamined. The power transfer capability of ICPT systems is an intricate function of the operational frequency, and thus resonant operations of the secondary side do not always guarantee maximizing the power transfer. A suitable control mechanism, such as the resonant frequency control, the variable frequency control, or the fixed frequency control, should be designed carefully according to the practical engineering requirement when the secondary capacitance varies.