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Flexible AC transmission system (FACTS) devices are widely recognized as powerful controllers to improve the dynamic performance and stability of power systems. The standard FACTS controllers are linear controllers designed around a specific operating point from a linearized system model with fixed parameters. However, at other operating points their performance degrades. Neural-network-based nonlinear intelligent control offers an attractive approach to overcome the drawbacks of the linear controllers. This paper presents two different neural-network-based intelligent control architectures, i.e., indirect adaptive neurocontrol and adaptive critic design based optimal neurocontrol, for designing the external control of an SSSC FACTS device. Simulation studies are carried out to evaluate the proposed nonlinear intelligent controllers on single machine infinite bus as well as multi-machine power systems. Results show that the proposed intelligent controls improve the dynamic performance of the SSSC and the associated power network.