In recent years, there have been many attempts to construct multiple-processor computer systems. The majority of these systems are based on von Neumann style uniprocessors. To exploit the parallelism in algorithms, any high performance multiprocessor system must, however, address two very basic issues-the ability to tolerate long latencies for memory requests and the ability to achieve unconstrained, yet synchronized, access to shared data. In this paper, we define these two problems, and examine the ways in which they are addressed by some of the current and past von Neumann multiprocessor projects. We then proceed to hypothesize that the problems cannot be solved in a von Neumann context. We offer the data flow model as one possible alternative, and we describe our research in this area.