This thesis is a study of the story in natural conversation. The story is an intuitively recognizable but problematic unit to describe, since the features which distinguish it in conversation are s~ markedly different from the features that characterise a narrative text. An attempt is made in the thesis to locate the study of stories in an area of research that allows analysis in terms )of the interaction of story-teller and addressees in a conversation. Within this area of linguistic research, which may broadly be termed pragmatics, some definitions of story-telling are examined which explicitly claim to be 'functional', that is, based on the asswnption that story-telling is an activity directed by the teller towards the achievement of certain goals. Such a definition is provided, for example, by Labov and Waletzky in their classic paper on oral versions of narrative, which is examined at some length in this thesis. It is concluded that a definition like the one offered by Labov and Waletzky is unsatisfactory when applied to stories in natural conversation despite the functional approach advocated. Two other approaches to the study of language use in so~ial interaction, however, appear to be suitable to the data at hand, which consists largely of tape-recorded conversations in English and Bengali. These�;:,approacbes seem initially to conflict sharply, but when investigated display important complementary aspects. In this thesis I endeavour to show that an integration of some of the basic notions which comprise the deductivist theory of speech acts with the empirical methodology of conversational analysis illuminates particular problems in my data in a way that neither approach : singly. can. Speech act theory is, of cour se, a generic term and the version of a speech act theory of communication-intention that I select as the most appropriate framework for- the practice of conversational analytic methodology is the Gricean one, which suggests a model based specifically on conversational interchange. Conversational analytic methods are used to observe some regularities wTuich distinguish the telling of stories within the turn-taking system of natural conversation. It is argued that the regularities observed by conversational analysis can be incorporated in a Gricean model by treating them as Lewisian conventions defining regularities of behaviour within a community. Theoretical reasons are given for this move, but perhaps the best reason for seeking such an integration remains that the stories which are the immediate focus of attention in this thesis are best understood thereby.