This paper focuses on developing a distributed leader-following fault tolerant tracking control scheme for a class of high-order nonlinear uncertain multi-agent systems. Neural network based adaptive learning algorithms are developed to learn unknown fault functions, guaranteeing the system stability and cooperative tracking even in the presence of multiple simultaneous process and actuator faults in the distributed agents. The time-varying leader’s command is only communicated to a small portion of follower agents through directed links, and each follower agent exchanges local measurement information only with its neighbors through a bidirectional but asymmetric topology. Adaptive fault-tolerant algorithms are developed for two cases, i.e., with full-state measurement and with only limited output measurement, respectively. Under certain assumptions, the closed-loop stability and asymptotic leader-follower tracking properties are rigorously established.