Presently some on-line vibration monitoring methods was used as an in-flight diagnostic and trend monitoring device. But very little work has been accomplished on the detection and quantification of combined gear damages and bearing faults in a bearing-rotor-gear transmission system. Vibrations caused by the combined damages in gears and bearing usually can not be identified readily without special procedure applied to the vibration signature. In this thesis, under a variety operating cases, vibration signature due to the combined damage between the outer race of bearing and the teeth of gear were examined in both time and frequency domains for identification purposes. Joint time-frequency analysis such as the Wigner-Ville Distribution (WVD) was used in detecting and identifying various types of gear and bearing damage. The modified Poincare Maps based on chaotic vibration were also successfully applied in analyzing the vibration from gear and bearing damages. The objective of this work is to develop an on-line Health Monitoring system to detect faults in gear and bearing. Considerable success has been achieved in this work to identify faults in both bearing and gear components.