In full-duplex systems, due to the strong self-interference signal, system nonlinearities become a significant limiting factor that bounds the possible cancellable self-interference power. In this paper, a self-interference cancellation scheme for full-duplex orthogonal frequency division multiplexing systems is proposed. The proposed scheme increases the amount of cancellable self-interference power by suppressing the distortion caused by the transmitter and receiver nonlinearities. An iterative technique is used to jointly estimate the self-interference channel and the nonlinearity coefficients required to suppress the distortion signal. The performance is numerically investigated showing that the proposed scheme achieves a performance that is less than 0.5dB off the performance of a linear full-duplex system.