In　this　paper,　we　present　an　internal　model　based　output　feedback　control　for　the　cooperative　semi-global　output　regulation　of　nonlinear　strict-feedback　multi-agent　systems　with　arbitrary　non-identical　relative　degrees　and　switching　network　topologies.　The　problem　is　first　converted　into　a　cooperative　semi-global　stabilization　problem　by　introducing　a　distributed　internal　model.　We　then　propose　a　distributed　output　feedback　stabilizer　that　is　determined　by　a　novel　distributed　observer　composed　of　a　distributed　dynamic　compensator　and　a　modified　reduced　order　high　gain　observer.　It　is　shown　that　this　novel　observer　is　capable　of　estimating　the　states　of　nonlinear　subsystems　with　arbitrary　non-identical　relative　degrees.　A　semi-global　common　Lyapunov　function　is　then　developed　for　conducting　the　stability　analysis　of　nonlinear　switched　closed-loop　system.　The　benefit　of　our　design　also　lies　in　that　it　has　removed　the　average　dwell　time　assumption　in　some　existing　literatures.　©　2019　Elsevier　Ltd