Conversation has recently become a focus of interest for speech act theory and several proposals have been formulated concerning the possible extension of speech act theory to the analysis of conversation. This debate (cf. Searle et al. 1992) has to be interpreted as a reactive move rather than as a natural extension of the domain of speech act theory. Nevertheless, this reaction, either sceptical (cf. Searle 1992) or optimistic (cf. Dascal 1992, Vanderveken 1992 and 1994), has brought interesting issues which contrast with the various attempts by linguists at extending speech act theory to the domain of discourse. The first purpose of this paper is to explicit the divergence between philosophers and linguists about the possible extension of speech act theory to discourse analysis. This paper has another purpose : it also deals with the possible domain of pragmatic theory with respect to discourse analysis. I shall argue that the main purpose of discourse analysis is the definition of necessary and sufficient conditions for sequencing and interpretating utterances in discourse. I claim that these two aspects of discourse (sequencing and interpretation) are intrinsically related and cannot be accounted for independently from each other. I claim furthermore that speech act theory cannot give any insight into the sequencing and interpretation problems, because speech act theory is neither a theory of interpretation (it is a theory of meaning) nor a global theory of action. Finally I show how a radical pragmatic theory (in the Gricean sense) accounts for the sequencing and interpretation problems.