An adaptive control scheme is developed for a class of single-input nonlinear systems preceded by unknown hysteresis, which is a non-differentiable and multi-value mapping nonlinearity. The controller based on the three-layer neural network (NN), whose weights are derived from Lyapunov stability analysis, guarantees closed-loop semiglobal stability and convergence of the tracking errors to a small residual set. An example is used to confirm the effectiveness of the proposed control scheme. An adaptive control scheme is developed for a class of single-input nonlinear systems preceded by unknown hysteresis, which is a non-differentiable and multi-value mapping nonlinearity. The controller based on the three-layer neural network (NN), whose weights are derived from Lyapunov stability analysis, guarantees closed-loop semiglobal stability and convergence of the tracking errors to a small residual set. An example is used to confirm the effectiveness of the proposed control scheme.