In this paper, the problem of identifying nonlinear systems under adaptive binary-valued output measurements is considered. We follow a nonparametric approach, which directly estimates the value of the nonlinear function representing the system at any fixed point with the help of a recursive kernel-based stochastic approximation algorithm with expanding truncations (SAAWET). The thresholds of the binary sensor are adaptively designed to achieve a sufficient richness of information in the output observations. The constructed estimates are proved to converge to the true values with probability one. Two numerical examples are given showing that the simulation results are consistent with the theoretical analysis.