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As the transmission power increases for high-power full-duplex (FD) communications, the nonlinear effects of the transmit chain become more significant, resulting in severe nonlinear self-interference (SI) at the receiver of the FD transceiver and hence demodulation performance degradation for the desired signal from a remote user. In this paper, a blind nonlinear SI cancellation method, which consists of a cancellation stage and a recovery stage, is proposed to cancel the nonlinear SI along with the linear SI signal for an orthogonal frequency division multiplexed (OFDM)-modulated FD transceiver. By taking the advantage of two symbols on adjacent subcarriers received in one OFDM symbol, the cancellation stage cancels both the linear SI and its nonlinear SI components of the received signal without estimating the transmitter nonlinearity as well as the SI channel response. Subsequently, the recovery stage is performed on the resulting signal of the cancellation stage to eliminate any impacts on the desired signal. Simulations are performed on a nonlinear model extracted from a practical class AB power amplifier with transmission power ranging from 10 to 30 dBm to demonstrate different nonlinear distortions. The effectiveness of the proposed nonlinear cancellation method is verified in terms of the computation complexity, the cancellation capability for the SI signal, and the bit error rate of the desired signal.