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. (C) 2019 Elsevier Ltd. All rights reserved.