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This technical note studies the consensus problem for cooperative agents with nonlinear dynamics in a directed network. Both local and global consensus are defined and investigated. Techniques for studying the synchronization in such complex networks are exploited to establish various sufficient conditions for reaching consensus. The local consensus problem is first studied via a combination of the tools of complex analysis, local consensus manifold approach, and Lyapunov methods. A generalized algebraic connectivity is then proposed to study the global consensus problem in strongly connected networks and also in a broad class of networks containing spanning trees, for which ideas from algebraic graph theory, matrix theory, and Lyapunov methods are utilized.