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This paper considers the leader-follower flocking problem of networked underactuated autonomous surface vehicles (ASVs) in the presence of uncertain dynamics. By employing the graph theory and neural networks, a distributed adaptive flocking controller is developed for the vehicles to achieve the motion synchronization with the leader. A collective potential function is used to avoid collisions between the vehicles. Based on Lyapunov stability analysis, the developed neural flocking algorithm guarantees that all the ASVs' headings and speeds are synchronous with the leader for any undirected connected communication network. Simulation results using an experimental ship model are given to show the efficacy of the proposed strategy.