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This paper considers the design of observer-based distributed adaptive controllers to achieve a leader-follower consensus for high-order nonlinear multi-agent systems in the presence of non-symmetric input saturation constraint and system uncertainties. Solving the consensus problem for nonlinear multi agent systems in the presence of unknown terms in the dynamics equations of follower that are due to model simplification, parameters uncertainty or external disturbances are investigated. In order to reduce the conservatism, the upper bound of uncertain term is considered to be unknown, which is obtained by adaptive laws. In addition, it is assumed that all states variables of agents are not directly measurable; therefore firstly, by designing the nonlinear distributed observers, the states variables of agents are estimated. Then, by using the sliding mode technique, the observer-based distributed adaptive control laws are designed to ensure the consensus between the agents, and the output of the followers can track the output of the leader, in the presence of non-symmetric input saturation and uncertain terms. Finally, the results of the simulations have completely confirmed the achievements of the proposed laws.