In　this　paper,　we　present　a　novel　universal　adaptive　output　feedback　control　for　the　cooperative　output　regulation　problem　of　linear　multi-agent　systems.　The　agent　plant　is　general　in　the　sense　that　those　interesting　practical　issues　such　as　unknown　dynamics,　direct　network　graph,　and　nonidentical　relative　degree　agents　are　taken　into　account　simultaneously.　The　obtained　controller　consists　of　the　reduced-order　observer,　the　internal　model,　as　well　as　the　adaptive　control　law,　all　of　which　are　shown　to　be　fully　distributed.　It　is　of　interest　to　see　that,　in　our　recursive　design,　each　agent　does　not　need　to　estimate　the　unknown　parameters　caused　by　the　neighbors,　giving　rise　to　a　merely　two-dimensional　adaptive　law　with　quite　a　simple　structure.　It　is　also　this　feature　that　our　design　has　the　capability　of　handling　the　agents　with　arbitrary　nonidentical　high　relative　degrees.　©　2018　IEEE.