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.　©　2018　Elsevier　Ltd