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This paper discusses the application of trajectory sensitivity analysis (TSA) of power systems containing FACTS compensators. Thyristor controlled series compensator (TCSC) and static synchronous compensator (STATCOM) are the devices considered. The TCSC is modeled by a variable capacitor, the value of which changes with the firing angle. The STATCOM is modeled by a voltage source connected to the system through a transformer. The effect of their individual and simultaneous use on the system transient stability is studied by applying TSA. Two different test systems are considered. It is shown that TSA can be used to determine the best possible locations of the two devices for transient stability improvement as well as to predict the critical clearing time.