  We consider networks of processes that all execute the same finite-state
protocol and communicate via a rendez-vous mechanism. When a process requests a
rendez-vous, another process can respond to it and they both change their
control states accordingly. We focus here on a specific semantics, called
non-blocking, where the process requesting a rendez-vous can change its state
even if no process can respond to it. In this context, we study the
parameterised coverability problem of a configuration, which consists in
determining whether there is an initialnumber of processes and an execution
allowing to reach a configuration bigger than a given one. We show that this
problem is EXPSPACE-complete and can be solved in polynomial time if the
protocol is partitioned into two sets of states, the states from which a
process can request a rendez-vous and the ones from which it can answer one. We
also prove that the problem of the existence of an execution bringing all the
processes in a final state is undecidable in our context. These two problems
can be solved in polynomial time with the classical rendez-vous semantics.
