In this paper, we present a schedulability analysis technique for distributed hard real-time systems in which responses to different events may synchronize with each other. This technique uses a representation model for distributed systems that allows us to describe not only the task synchronization due to resource sharing, but also the activation due to combinations of events or the generation of several events by a single task. The model is representative of a large number of systems and is suitable for the treatment of message-passing systems or the client-server architecture. The analysis technique is based on the existing RMA techniques for analyzing distributed real-time systems; it allows obtaining upper bounds for the worst-case response times of the system, thus allowing us to make guarantees about the fulfillment of the timing requirements that have been imposed.