Some more recent lines of research converge on claiming that human cognitive behavior in general and linguistic discourse in particular cannot reasonably be reduced to one monolithic system of cognitive activity. What this research suggests, rather, is that this behavior exhibits a dualistic organization. In the present paper, two frameworks representing this tradition are contrasted, namely Discourse Grammar and the dual process model. The former rests on observations on language structure and language use, while the latter was developed on the basis of neurolinguistic observations. The two frameworks converge on claiming that there is a significant correlation between linguistic categorization and hemisphere-based brain activity. The present paper argues that this correlation can be related to contrasting linguistic functions associated with each of the two hemispheres.