Ongoing processes require a metaphysical conception of time according to which the world is existentially dynamic. Within the framework of the growing block theory of time, a crucial question emerges concerning the precise nature of becoming in a growing block universe: What exactly happens at the edge of becoming? Does a process constitute an expanding whole – complete yet growing – or is a dynamic processual entity inherently incomplete due to open-endedness? In this talk we want to discuss whether what is situated at the edge of becoming is not yet a temporal part of the (therefore open-ended) process, but rather transforms into its temporal part immediately afterwards. Then, the process is either still ongoing or it has gone on. Through this interpretation, of what dynamic processes are/do at the edge of becoming, open-endedness may not require or constitute an incompleteness of the growing block universe.