A full-duplex transceiver is provided with componentry and methods for cancellation of nonlinear self-interference signals. The transceiver is capable of receiving an incoming radio-frequency signal that includes both a desired radio-frequency signal component and a self-interference component caused by the transceiver's own radio-frequency transmission. The transceiver demodulates the incoming radio-frequency signal to generate a first demodulated signal. The transceiver combines an analog corrective signal with the first demodulated signal to generate a second demodulated signal with reduced self-interference. The transceiver processes the first and second demodulated signals to determine a desired incoming baseband signal and to determine nonlinear components of the self-interference signal, such as nonlinearities introduced by the transceiver's power amplifier.