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This paper considers the containment control of networked autonomous underwater vehicles guided by multiple dynamic leaders over a directed network. Each vehicle is subject to model uncertainty and unknown time-varying ocean disturbances. A new predictor-based neural dynamic surface control design approach is presented to develop the adaptive containment controllers, under which the trajectories of vehicles converge to the convex hull spanned by those of the leaders. Specifically, iterative neural updating laws, based on prediction errors, are constructed, which enable the accurate identification of the unknown dynamics for each vehicle, not only in steady state but also in transient state. Furthermore, this result is extended to the output-feedback case where only the position-yaw information can be measured. A neural observer is developed to recover the unmeasured velocity information. Based on the observed velocities of neighboring vehicles, distributed output-feedback containment controllers are devised, under which the containment can be achieved regardless of model uncertainty, unknown ocean disturbances, and unmeasured velocity information. For both cases, Lyapunov–Krasovskii functionals are used to prove the uniform ultimate boundedness of the closed-loop error signals. Comparative studies are given to show the performance improvement of the proposed methods. [ABSTRACT FROM AUTHOR]