Summary: In this paper, we develop nonlinear distributed or semi-decentralized cooperative control schemes for a team of heterogeneous Autonomous Underwater Vehicles (AUVs). The objective is to have the network of AUVs follow a desired trajectory, while the agents maintain a desired formation when there is a virtual leader whose position information is only available and known to a very small subset of the agents. The virtual leader does not receive any feedback and information from the other agents and the agents only communicate with their nearest neighboring agents. It is assumed that the model parameters associated with each vehicle/agent are different, although the order of the agents is the same. The developed and proposed nonlinear distributed cooperative control schemes are based on the dynamic surface control methodology for a network of heterogeneous autonomous vehicles with uncertainties. The development and investigation of the dynamic surface control methodology for a team of cooperative heterogeneous multi-agent nonlinear systems is accomplished for the first time in the literature. Simulation results corresponding to a team of six AUVs are provided to demonstrate and illustrate the advantages and superiority of our proposed cooperative control strategies as compared to the methods that are available in the literature.