Auxiliary power unit (APU) is a gas turbine engine on aircraft that provides energy for functions other than propulsion. Its starter is a crucial component that outputs assistant power to support the APU starting process. Starter performance degradation significantly impairs the whole APU life and raises risks for the aircraft flight. However, the current maintenance policy for the starter is still "run it till it breaks". An effective technique for the starter diagnostics and prognostics has not been reported yet. The aim of this thesis is to propose a framework for enabling the online detection and prediction of starter degradation. For this purpose, the thesis makes use of a dataset containing information about 52 APU "inability to start" failure events that were collected from actual aircraft operations over a period of ten years. Through the establishment of the relationship between the starter degradation and gas turbine engine starting performance, 13 of these 52 failures were identified as being caused by the starter degradation. Once this determination has been made, an online classifier based on moving autocorrelation is designed to detect the initial phase of degradation for each failure. Finally, a particle filtering based approach with an associated system state model is proposed to achieve the fault diagnostics and failure prognostics. The results demonstrate that a condition based maintenance program for the APU starter can be implemented to avoid unnecessary economic losses and to enhance aircraft operating safety. i First and foremost, I would like to express my deepest gratitude to my supervisor Dr. LIU Jie for his enthusiastic supervision and patient guidance. He is the best supervisor I had ever met, with encourage, enthusiasm, and immense knowledge. He supported and guided me throughout the entire master program. Without him, it would not have been possible to have this thesis. Also, I would like to sincerely thank our research collaborator Dr. YANG Chunsheng from National Research Council Canada for his insights and nice helps in this two-year project.