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In this paper, a fault-tolerant control scheme is proposed for the rigid spacecraft attitude control system subject to external disturbances, multiple system uncertainties, and actuator faults. The angular velocity measurement is unavailable, which increases the complexity of the problem. An observer is first designed based on the super-twisting sliding mode method, which can provide accurate estimates of the angular velocity in finite time. Then, an adaptive fault-tolerant controller is proposed based on neural networks using the information from the observer. It is shown that the attitude orientations converge to the desired values exponentially. Finally, a simulation example is utilized to verify the effectiveness of the proposed scheme.