In　this　paper,　we　study　the　cooperative　global　robust　output　regulation　problem　for　nonlinear　multi-agent　systems　in　lower　triangular　form　under　directed　graph.　We　first　establish　a　few　technical　lemmas　for　laying　the　foundation　of　a　block　global　backstepping　approach,　and　then,　under　some　standard　assumptions　on　the　system　dynamics　and　the　graph　topology,　we　solve　the　problem　via　a　distributed　control　law　by　combining　the　internal　model　technique　with　a　distributed　gain　assignment　technique.　Our　result　contains　a　few　existing　results　as　special　cases.