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This article aims to propose a Self-Recurrent Wavelet Neural Adaptive Supplementary Controller (SRWNASC) design of Static Synchronous Series Compensator (SSSC) for inter-area oscillations damping. The proposed approach employs the SRWNN as two distinct sub-networks namely; the SRWNN-Identifier (SRWNNI) and the SRWNN-Controller (SRWNNC), based on the indirect adaptive control theory. To guarantee the convergence of the proposed control scheme, the parameters of both the SRWNNI and the SRWNNC are updated online employing a stable Back-Propagation (BP) training algorithm with Adaptive Learning Rates (ALRs) based on Discrete Lyapunov Stability Theorem (DLST). A two-machine two-area power system is used to show the effectiveness of the proposed approach for damping the inter-area oscillations.