The　cooperative　global　adaptive　output　regulation　of　nonlinear　multi-agent　systems　with　unity　relative　degree　was　studied　recently　for　the　case　where　the　inverse　dynamics　of　the　follower　subsystems　are　input-to-state　stable　(ISS).　In　this　paper,　we　present　a　further　result　by　relaxing　the　ISS　assumption　to　the　integral　ISS　(iISS)　assumption.　As　the　iISS　condition　is　strictly　weaker　than　the　ISS　condition,　our　result　applies　to　a　larger　class　of　nonlinear　multi-agent　systems.