A control scheme for nonlinear single input systems is introduced, where the controller has two modes of operation : In the first mode the controller is designed to achieve stability and performance in a neighborhood of the operating point where the system is operated under normal conditions. In the second mode the controller acts as a "safety jacket" that is designed to bring the system state back to the normal operating regime if unusually large disturbances force the system far from its normal mode of operation. The second mode is based on a very robust adaptive nonlinear high-gain feedback law. We prove that global asymptotic stability is achieved robustly with this scheme.