Unsolvability of the unboundedness problem for specification models allowing fifo channels was proved a few years ago by Brand and Zafiropulo. The paper investigates a testing approach of that problem. Instead of reducing the model in order to give decidability results, we work with the largest possible framework. We find a sufficient condition for unboundedness based on a relation between reachable global states. This gives a testing procedure which can be applied as well to communicating finite state machines as to Fifo-Nets. Moreover, the test extends existing decidability results. In fact it becomes a decision procedure for a class of systems strictly including linear and monogeneous systems. A few modifications of the relation make it available for Estelle specifications.