<p>In this paper, the containment control problem of output feedback nonlinear multi-agent systems (MASs) with unmodeled dynamics and asymmetric time-varying output constraints is studied. The high-gain K-filters are constructed to estimate the unmeasurable system states. In order to successfully handle the output constraints, two constraint functions are created to convert them into the error constraints. Using the properties of Gaussian function and introducing dynamic signals, the unmodeled dynamics and non-strict feedback terms are effectively processed. The dynamic event-triggered control (DETC) is applied to nonlinear multi-agent systems to reduce unnecessary communication. A novel adaptive output feedback containment control is developed by combining the dynamic surface approach with command filtered backstepping technique. Through Lyapunov stability analysis, it is proved that all signals in the closed-loop system are bounded, the outputs of all followers converge to a convex hull composed of the outputs of all leaders, and the Zeno phenomenon can be avoided. Finally, the simulation results verify the effectiveness of the proposed control strategy.</p>