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Two distributed consensus problems, including leadless consensus and tracking consensus, for multiple quadrotors with bounded disturbances under a directed topology are solved in this study. First, the model of a single quadrotor is divided into two subsystems. Some coupling terms between the two subsystems are regarded as external perturbations. For the case of leadless consensus, a distributed sliding-mode controller for the first subsystem and a state-feedback controller for the second subsystem are proposed to guarantee that the consensus is achieved with bounded errors that are only associated with disturbances. For the case of tracking consensus, by using the proposed sliding-mode consensus protocols combining with two sliding-mode observers, it is shown that all quadrotors can track the leader with bounded errors which can be manipulated suitably. Simulations show the effectiveness of the proposed control protocols.