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This technical note presents a cyclic-small-gain approach to distributed output-feedback control of nonlinear multi-agent systems. Through novel distributed observer and control law designs, the closed-loop multi-agent system is transformed into a large-scale system composed of input-to-output stable (IOS) subsystems, the IOS gains of which can be appropriately designed. By guaranteeing the IOS of the closed-loop multi-agent system with the recently developed cyclic-small-gain theorem, the outputs of the controlled agents can be driven to within an arbitrarily small neighborhood of the desired agreement value under bounded external disturbances. Moreover, if the system is disturbance-free, then asymptotic convergence can be achieved. Interestingly, the closed-loop distributed system is also robust to bounded time-delays of exchanged information.