Nowadays a lot of interest in Systems Theory is directed to problems in which separate systems are coupled to each other. We study the dynamics of a population of uniformly all-to-all coupled limit cycle oscillators. The oscillators are permitted to possess different natural frequencies. Our greatest interest goes out to the synchronization of such populations consisting of finitely many oscillators. This synchronized behaviour is only present if the strength of the interactions supersedes some threshold value. We try to obtain some stability properties of this behaviour
