This paper investigates the problem of distributed adaptive PI consensus tracking control for output-constrained nonlinear multiagent systems (MASs) with unknown control directions and unknown time-varying actuator faults under the directed graph. Firstly, an auxiliary filter network is constructed to estimate the output of the leader. Then, by introducing a nonlinear state transformation function, the asymmetric constraints on agents' outputs can be achieved with unconstrained initial conditions. Furthermore, based on the Nussbaum-type functions, a distributed adaptive PI controller is designed by utilizing the constructed generalized error for nonlinear MASs with unknown time-varying control directions caused by actuator faults. It is proved that the proposed control scheme can guarantee that all signals in the closed-loop system are bounded and the distributed asymptotic consensus tracking is achieved. Finally, a simulation example illustrates the effectiveness of the proposed control strategy.