Good scheduling policies for distributed embedded applications are required for meeting hard real time constraints and for optimizing the use of computational resources. We study the quasi-static scheduling problem in which (uncontrollable) control flow branchings can influence scheduling decisions at run time. Our abstracted task model consists of a network of sequential processes that communicate via point-to-point buffers. In each round, the task gets activated by a request from the environment. When the task has finished computing the required responses, it reaches a pre-determined configuration and is ready to receive a new request from the environment. For such systems, we prove that determining existence of quasi-static scheduling policies is undecidable. However, we show that the problem is decidable for the important sub-class of “data branching” systems in which control flow branchings are due exclusively to data-dependent internal choices made by the sequential components. This decidability result—which is non-trivial to establish—exploits ideas derived from the Karp and Miller coverability tree [8] as well as the existential boundedness notion of languages of message sequence charts [6].