This paper proposes a sound procedure to verify properties of communicating session automata (csa), i.e., communicating automata that include multiparty session types. We introduce a new asynchronous compatibility property for csa, called k-multiparty compatibility (k-mc), which is a strict superset of the synchronous multiparty compatibility used in theories and tools based on session types. It is decomposed into two bounded properties: (i) a condition called k-safety which guarantees that, within the bound, all sent messages can be received and each automaton can make a move; and (ii) a condition called k-exhaustivity which guarantees that all k-reachable send actions can be fired within the bound. We show that k-exhaustivity implies existential boundedness, and soundly and completely characterises systems where each automaton behaves equivalently under bounds greater than or equal to k. We show that checking k-mc is pspace-complete, and demonstrate its scalability empirically over large systems (using partial order reduction).Definition 5 (Stable). S has the stable property ( sp) if @s P RS pSq : Dpq; ǫq P RS pSq : s Ý Ñ˚pq; ǫq.A system has the stable property if it is possible to reach a stable configuration from any reachable configuration. This property is called deadlock-free in [22]. The stable property implies the eventual reception property, but not safety (e.g., an automaton may be waiting for an input in a stable configuration, see Example 2), and safety does not imply the stable property, see Example 4.Example 2. The following system has the stable property, but it is not safe. M s : pq!b pq!a M q : pq?a pq?b qr!c M r : qr?cNext, we define two properties related to bound independence. They specify classes of csa whose branching behaviours are not affected by channel bounds.Definition 6 (k-obi). S is k-output bound independent (k-obi), if @s " pq; wq P RS k pSq and @p P P, if s pq!a ÝÝÑ k , then @pq p , pr!b, q 1 p q P δ p : s pr!b ÝÝÑ k .