This paper is concerned with the global analysis of asymptotic synchronization of outputs in networks of identical oscillators. The oscillator models are assumed to possess a cyclic feedback structure. Such networks of oscillators abound in biochemistry, and are exemplified by circadian rhythm and cardiac cell networks. The main result exploits an incremental output feedback passivity property of cyclic feedback systems to prove global asymptotic output synchronization in a network composed of identical cyclic feedback systems. This result is illustrated on a network of Goodwin oscillators.