This paper studies the problem of global robust distributed output consensus of heterogeneous leader–follower multi-agent nonlinear systems by general directed output interactions. For a class of minimum-phase single-input single-output nonlinear agents having unity relative degree, it is shown that the problem is solvable by an internal model approach under certain mild conditions. A Lyapunov function based output-feedback control law is developed by converting the global output consensus into a global distributed stabilization problem for an augmented network.