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Near-field resonant-based wireless power transfer (WPT) technology has a significant impact in many applications ranging from charging of biomedical implants to electric vehicles (EVs). The design of robust WPT systems is challenging due to its position-dependent power transfer efficiency (PTE). In this paper, a new approach is presented to address WPT's strong sensitivity to the coupling factor variation between the transmit and receive coils. The introduced technique relies on harnessing the unique properties of a specific class of nonlinear resonant circuits to design position-insensitive WPT systems that maintain a high PTE over large transmission distances and misalignments without tuning the source's operating frequency or employing tunable matching networks, as well as any active feedback/control circuitry. A nonlinear-resonant-based WPT circuit capable of transmitting 60 W at 2.25 MHz is designed and fabricated. The circuit maintains a high PTE of 86% over a transmission distance variation of 20 cm. Furthermore, transmit power and PTE are maintained over a large lateral misalignment up to ±50% of the coil diameter and angular misalignment up to ±75°. The new design approach enhances the performance of WPT systems by significantly extending the range of coupling factors over which both load power and high PTE are maintained.