The digital circuits (i.e. the boolean systems) have been widely studied informally in electronics. Asynchronicity represents that general case in this study when each computation is made independently on the other computations. And commutativity is the weakest request that we have found, defined in [1] as: ’if two transitions can occur in either order from a given state, then there is at least one common resulting state which is independent of the order’. We identify the boolean asynchronous systems with the functions  : f0; 1gn ! f0; 1gn and our main concern is to formalize the concept of commutative system, using the framework from [2]. Some conclusions are presented.