Damping of power system plays an important role in not only increasing the transmission capacity but also in stabilizing the power system, especially after critical faults. Static Var Compensator (SVC) is a shunt FACTS device which has capability of fast and continuous capacitive and inductive reactive power supply to the power system. SVCs are widely used for voltage stability but studies show that they are also effective in providing damping to the system. In this thesis, three types of SVC damping controllers are designed. The first damping controller is an optimal linear controller in which the parameters of a damping controller are optimized using two swarm inspired algorithms namely; Particle Swarm Optimization (PSO) and Small Population based Particle Swarm Optimization. The second damping controller is an indirect adaptive based neurocontroller (NC). This controller comprises of a Wide Area Monitor (WAM). The WAM and NC are realized using a neural structure called the Dual Function Neuron (DFN). A DFN requires shorter training time and can still maintain its fault tolerant capabilities for any complex problem. The components realized using DFNs are trained using PSO algorithm. The third controller design is an optimal NC based on Heuristic Dynamic Programming which is a part of Adaptive Critic Designs (ACDs). This design comprises of a WAM, a critic network and a controller. All these are realized using the DFN structure and trained using PSO. Results comparing the performance of designed controllers with the linear controller (tuned by trial and error) are presented based on PSCAD and RSCAD environment studies. Several analyses are presented for each of the controller to show the frequency and the damping of the dominant modes of the system --Abstract, page iii