This research analyzes the linkage between power system disturbances and failures in relaying systems. The annual disturbance reports prepared by the North American Electric Reliability Council were examined. It has been found that relaying system failures plays very important role in power system cascading outages. The type of relaying system failures that are the most troublesome are the ones that have a potential to remain hidden until being exposed by some abnormal power system states to trigger relay misoperations. Each commonly used relaying scheme in transmission system is examined for any hidden failures that can lead to relay misoperations and multiple power system contingencies. Each hidden failure mode has a region, called region of vulnerability. Inside this region, some abnormal power system states can expose the hidden failure. The reach of the region depends largely on the settings of the relay in question. A method of computing the relative importance of each region of vulnerability, called vulnerability index, was proposed. The calculation of the index can be based on some measurements of power system performances. In this research, the stability measurements of the system following some contingencies that may occur in the region are chosen. With this approach, vulnerable relays can be identified. A preventive method was proposed so that the number of relay misoperations due to hidden failures and, ultimately, the number of power system disturbances can be reduced. / Ph. D.