This dissertation addresses monitoring of nonlinear systems for detection and prediction of incipient instabilities. The analysis and design presented here rely on the influence of noise on system behavior near the onset of instability. The work is of relevance to high performance engineering systems, which are often operated with a low stability margin in order to maximize performance. In such a stressed operating mode, a small or moderate disturbance can result in loss of stability of the nominal operating condition. This can be followed by operation in a new lower performance mode, oscillatory behavior, or even system collapse. All of these conditions can be viewed as bifurcations in the underlying dynamical models. Prediction of the precise onset points of these instabilities is made difficult by the lack of accurate models for complex engineering systems. Thus, in this thesis monitoring systems are proposed that can signal an approaching instability before it occurs, without requiring a precise system model. The approach taken in this work is based on precursors to instability that are features of the power spectral density of a measured output signal. The noise in the system can be naturally occurring noise or can be intentionally injected noise. The output signal can be measured directly from the physical system or from the system with an augmented monitoring system. Design of appropriate augmented monitoring systems is a major topic of this work. These monitoring systems result in enhancing precursor signals and also allow control of the precursor by tuning external parameters. This tuning is important in that it adds confidence to the detection of an impending instability. The methods developed on precursors for instablility are applied to models of axial flow compression systems. Existing results on bifurcations for such models and their relation to compressor stall provide a starting point for the analysis.