This chapter considers the distributed adaptive neuro-fuzzy output feedback control protocol design to solve the output synchronization problem for heterogeneous multiagent systems with nonlinear strict-feedback agent dynamics. The output constraints and actuator saturation are considered simultaneously. First, a distributed high-gain observer is employed to estimate the unmeasured agent state and relax the requirement of the Lipschitz continuity of nonlinear follower dynamics. Second, an asymmetric barrier Lyapunov function with time-varying constraints is presented to deal with both the transient and the steady-state constraints on the output synchronization error. To deal with the actuator saturation, a distributed auxiliary dynamical system is designed for each follower. The fuzzy logic system is employed to compensate for the uncertain follower dynamics with guaranteed semi-global uniformly ultimate boundedness of all closed-loop signals. Finally, a simulation example is conducted to verify the efficacy of the presented adaptive neuro-fuzzy controller design.