In earlier work it was shown that, given two consistent timed scenarios, there might not exist a scenario whose semantics is the union of those of the two. A sufficient condition for the non-existence of such a union was also identified. In this paper we report on a comprehensive study of the union operation for scenarios. We identify a new sufficient condition that provides a syntactic criterion for the existence of a scenario that is the union of two given scenarios. We also prove that the condition is necessary.