Formal specifications of protocol-oriented agent interactions have focused mainly on the semantics of the constituent agent communication language (ACL).We argue that a proper theoretical treatment of conversations cannot be simply derived compositionally from the semantics of individual Communicative Acts (CAs). Accordingly, we develop a theory of joint conversations that is independent of its constituent CAs. We treat the process of a group following an interaction protocol as a persistent joint communicative action (JCA) by the group. We define compliance in a joint conversation and we prove salient properties of joint conversations.