A number of concepts that play a central role in Cognitive Grammar (CG) can be invoked in the analysis of discourse. Foremost amongst these are the notions of 'frame', 'profile' and 'radial category'. Such concepts are normally illustrated in CG with respect to lexical items in isolation from actual contexts of use. They can, however, shed light on communicative processes in real conversation. This claim is illustrated through the analysis of data from family arguments. Sources of argument and disagreement are traced to competing frames and construals (associated with the concept of radial category structure) applied by each of the participants in the discourses examined. The study suggests that CG has the potential to develop into a powerful tool for discourse analysis.