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This paper investigates the distributed fault-tolerant consensus tracking problem of nonlinear multi-agent systems with general incipient and abrupt time-varying actuator faults under cyber-attacks. First, a decentralized unknown input observer is established to estimate relative states and actuator faults. Second, the estimated and output neighboring information is combined with distributed fault-tolerant consensus tracking controllers. Criteria of reaching leader-following exponential consensus tracking of multi-agent systems under both connectivity-maintained and connectivity-mixed attacks are derived with average dwelling time, attack frequency, and attack activation rate technique, respectively. Simulation example verifies the effectiveness of the fault-tolerant consensus tracking algorithm.