In this paper, the nonparametric identification of nonlinear systems with binary-valued output observations is considered. The kernel-based stochastic approximation algorithm with expanding truncations (SAAWET) is proposed to recursively estimate the value of a nonlinear function representing the system at any fixed point. All estimates are proved to converge to the true values with probability one. A numerical example, which shows that the simulation results are consistent with the theoretical analysis, is given. Compared with the existing works on the identification of dynamic systems with binary-valued output observations, here we do not assume the complete knowledge of the system noise and the system itself is non-parameterized. On the other hand, we assume that we can adaptively design the threshold of the binary sensor to achieve a sufficient richness of information in the output observations.