A reliable and robust diagnostic / prognostic system is very useful for health condition monitoring of rotary machinery such as gearboxes. Such a system can provide early warnings of malfunction or possible damage to avoid sudden failures, and to allow effective repair and maintenance. Currently, there are many methods that can be used to monitor the health condition of gearboxes, but each has its advantages and disadvantages. This thesis presents a comprehensive investigation to assess the sensitivity and robustness of well-accepted gear fault detection techniques. Test results show that the beta kurtosis, continuous wavelet transform, and phase demodulation are the most promising fault detection techniques. A neuro-fiizzy diagnostic system is then developed whereby the strengths of the above signal processing techniques are integrated to provide a more positive assessment of a gear’s health condition. Reference functions are proposed to further enhance signature characteristics and to facilitate the automatic diagnostics. A constrained-gradient-reliability algorithm is proposed to train fuzzy membership functions and rule weights. In order to further improve the diagnostic reliability, a neuro-fiizzy prognostic system is developed. Tests demonstrate that the developed neuro-fiizzy prognostic system is a very reliable and robust online predictor. It can capture system dynamic behaviour quickly and accurately. In addition, this thesis proposes a new technique, via gear health condition monitoring, for rotation error detection in multistage printing presses. A novel approach is developed to determine gear runout based on the signal from magnetic pickups. The viability of these techniques is verified through experimental testing.