This　paper　focuses　on　robust　nonlinear　coordination　of　heterogeneous　uncertain　second-order　multi-agent　systems　subject　to　directed　communication　topologies.　We　develop　a　nonlinear　internal　model　principle　based　approach　for　the　problem　in　a　framework　of　cooperative　global　robust　output　regulation,　independent　of　the　a　priori　of　the　leader　dynamics　information　except　its　order.　As　a　major　consequence,　this　study　assures,　by　means　of　establishing　a　strict-Lyapunov　function　for　the　closed-loop　system,　not　only　a　specified　exponential　convergence　rate　but　also　tolerable　bounds　of　unmodeled　disturbances.　Hence,　the　former　guarantees　an　appealing　performance　and　the　latter　an　important　robustness　property.　(C)　2018　Elsevier　Ltd.　All　rights　reserved.