[en] The phenomenon of linear mode conversion can undergo a qualitative change when one of the modes is weakly nonlinear. Its nonlinear wave-number shift can overcome the dephasing due to plasma nonuniformity if the incident action-flux exceeds a threshold. This process has been called spatial autoresonance. The authors study a simple model analytically and numerically for all the different physical regimes: positive or negative coupling between the waves, positive or negative energy waves, and positive or negative nonlinearities. Some of these cases have unstable solutions, where convective saturation is replaced by unbounded convective growth, linear with distance