Speech acts are generally held to have cognitive effects (the hearer's recognition of the meaning and force of the speech act). The author takes the opposite view (which, to some extent, goes back to Austin) that it is essential to speech acts, qua illocutionary acts, to have conventional effects on the interactional situation (such as assignments of obligation or entitlement). She then supplements speech act theory with a conception, inspired by narrative semiotics, of an action as a move in a sequence and reassess the role of action in the cognitive and interactional dynamics of speech act sequences. It is further claimed that the "narrative scheme" proposed by Greimas is part of the competence by which we understand sequences of speech acts. Two conversational sequences are discussed as examples.