This paper studies the event-triggered cooperative global robust output regulation problem for a class of nonlinear multi-agent systems via a distributed internal model design. We show that our problem can be solved practically in the sense that the ultimate bound of the tracking error can be made arbitrarily small by adjusting a design parameter in the proposed event-triggered mechanism. Our result offers a few new features. First, our control law is robust against both external disturbances and parameter uncertainties, which are allowed to belong to some arbitrarily large prescribed compact sets. Second, the nonlinear functions in our system do not need to satisfy the global Lipschitz condition. Thus our systems are general enough to include some benchmark nonlinear systems that cannot be handled by existing approaches. Finally, our control law is a specific distributed output-based event-triggered control law, which lends itself to a direct digital implementation. (C) 2018 Elsevier Ltd. All rights reserved.