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An approximation-based adaptive fault-tolerant (AFT) control problem is investigated for strict-feedback non-linear systems with unknown time-delayed non-linear faults. The error surfaces restricted by prescribed performance bounds are employed to guarantee the transient performance at the moment when faults with unknown occurrence time and magnitude occur. Based on the surfaces, we design a memoryless AFT control system where the function approximation technique using neural networks is applied to adaptively approximate unknown non-linear effects and changes in model dynamics because of the time-delayed faults. It is shown from Lyapunov stability theorem that the tracking error of the proposed control system is preserved within the prescribed performance bound and converges to an adjustable neighbourhood of the origin regardless of unknown time-delayed non-linear faults.