An online approach to nonlinear system identification based on binary observations is presented in this paper. This recursive method is a nonlinear extension of the LMS-like (least-mean-squares) basic identification method using binary observations (LIMBO). It can be applied in the case of weakly nonlinear Duffing oscillator coupled with a linear system characterized by a finite impulse response. It is then possible to estimate both Duffing and impulse response coefficients knowing only the system input and the sign of the system output. The impulse response is identified up to a positive multiplicative constant. The proposed method is compared in terms of convergence speed and estimation quality with the usual LMS approach, which is not based on binary observations.