In　this　paper,　we　study　the　cooperative　semi-global　output　regulation　problem　for　a　class　of　nonlinear　strictfeedback　multi-agent　systems,　where　the　subsystems　are　assumed　to　have　nonidentical　relative　degrees.　We　first　introduce　the　so-called　distributed　internal　model　that　converts　our　problem　into　the　cooperative　semi-global　stabilization　problem　of　the　corresponding　augmented　system　composed　of　the　original　multi-agent　system　and　the　internal　model.　We　then　put　this　augmented　system　into　the　general　block　lower　triangular　form,　and　develop　the　block　semi-global　backstepping　technique　to　stabilize　it.　Comparing　with　some　existing　literatures,　our　design　has　removed　the　identical　relative　degree　assumption,　and　hence　applies　to　a　much　larger　group　of　nonlinear　multi-agent　systems.