This brief paper presents a distributed adaptive fault-tolerant leader-following consensus control scheme for a class of nonlinear uncertain multi-agent systems under a bidirectional communication topology with possibly asymmetric weights and subject to process and actuator faults. A local fault-tolerant control (FTC) component is designed for each agent using local measurements and suitable information exchanged between neighboring agents. Each local FTC component consists of a fault diagnosis module and a reconfigurable controller module comprised of a baseline controller and two adaptive fault-tolerant controllers activated after fault detection and after fault isolation, respectively. By using an appropriately chosen Lyapunov function, the closed-loop stability and asymptotic convergence property of leader–follower consensus are rigorously established under different operating modes of the FTC system.