Abstract Full duplex (FD) communication is a promising solution for enhancing the data rates of wireless networks, thanks to the simultaneous bilateral spectral use. Nevertheless, FD communication is still challenged by the self-interference (SI) problem. Existing linear SI cancellation techniques to fight this challenge are observed to be less effective at relatively higher power levels, due to the nonlinear behavior introduced by the transmitter and receiver hardware. In this paper, we propose an effective nonlinear digital cancellation solution and demonstrate its performance on a real software defined FD radio set-up. The proposed nonlinear solution is based on a memory polynomial model, which is also integrated with linear cancellation and both are implemented at the baseband level. The performance of the FD radio with integrated nonlinear and linear cancellation is observed via laboratory tests, as well as tests with a channel emulator under time varying channel conditions. It is shown that the proposed nonlinear cancellation provides about 3 dB improvement over linear only cancellation at low and moderate power levels, and up to 5 dB improvement at high power levels without any modification to hardware, unlike the existing methods. The proposed nonlinear cancellation does not introduce any extra communication overhead, since nonlinear coefficients are estimated only once for each transmit power level, stored and reused. Under time varying channel conditions, the performance of nonlinear estimation and cancellation is affected only by the performance of linear channel estimation, which can be addressed by choosing the packet size in accordance with channel coherence time.