A simplified version of an Adaptive Neuro-Fuzzy Controller (ANFC) applied to a FACTS device, namely a Static VAr Compensator (SVC), is presented in this dissertation. The proposed Adaptive Simplified Neuro-Fuzzy Controller (ASNFC), used as a supplementary controller to damp power system oscillations, consists of a reduced number of input Membership Functions (MFs) and Consequent Parameters (CPs). Unlike the common techniques of using the generator speed or the power angle deviations as inputs to the controller, the input to the ASNFC is the power deviation at the bus where the SVC is located. A Neuro Identifier is used to track the behaviour of the system in real-time and update the controller on-line. The effectiveness of the proposed controller is tested on a single machine infinite bus system, and a multi-machine system. Results of simulation studies demonstrate that the performance with the proposed ASNFC is practically the same as with ANFC, but with a smaller number of parameters to optimize that reduces computation time for real-time application. In addition, the proposed ASNFC is further tested on a physical model power system where the controller is applied to the generation unit. The results obtained indicate a successful implementation of the ASNFC in damping power system oscillations over the Conventional Power System Stabilizer (CPSS). Furthermore, similar dynamic performance is provided by the ASNFC, as compared to the detailed ANFC.