Power system stability can significantly be enhanced by installing a Static Synchronous Series Compensator (SSSC) using appropriate damping control scheme. In this work, a new Online Adaptive Legendre Wavelet (OALeW) based NeuroFuzzy control of SSSC is proposed. The proposed control strategy tunes the rule base using the current estimate of plant model, based on the online sensitivity measure, provided by the identification block. The parameters of the controller are updated online using gradient descent based backpropagation algorithm. The robustness of the proposed control strategy is validated using nonlinear time domain simulations and different performance indices for Single Machine Infinite Bus (SMIB) and multimachine test systems. A comparative analysis with singleton Takagi-Sugeno-Kang (TSK) reveals that the proposed OALeW control performs better in both the transient and steady-state regions for different operating conditions and faults with improvement in control effort smoothness.