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Bernd Heine, Tania Kouteva/Kuteva and Gunther Kaltenböck The present paper compares the two modes of processing proposed by Van Lancker Sidtis (2009) in her dual process model and the two domains of discourse organization distinguished in the framework of Discourse Grammar (Heine et al. 2013; Kaltenböck et al. 2011). These two frameworks were developed on different kinds of data. In the dual process model it is observations on patients with left or right hemisphere damage that marked the starting point of analysis. Central to the dual process model is the distinction between novel speech (or novel language, or newly created language, or propositional speech) and formulaic speech (or formulaic expressions or automatic speech). Easily identified instances of formulaic speech are swear words, interjections, pause fillers, discourse elements, non-literal lexical meanings for idioms, proverbs. Unlike the dual process model, in the Discourse Grammar model it is linguistic discontinuities that provided the basis of analysis. Discourse grammar in this model is understood as all the linguistic resources that are available for constructing spoken and written (and signed) texts. We argue that Discourse Grammar can be divided into two distinct domains, namely Sentence Grammar and Thetical Grammar. Whereas Sentence Grammar has been at the centre of interest in mainstream linguistics, Thetical Grammar encompasses linguistic phenomena – such as formulae of social exchange, imperatives, vocatives, interjections, including hesitation markers and pause fillers and what is traditionally known as “parenthetical” constructions – that pose a problem to orthodox grammatical analysis. We show that the findings made within the two frameworks are largely compatible with one another: both models converge on claiming that there is a significant correlation between linguistic categorization and hemisphere-based brain activity. In the dual process model it is hypothesized that there is a significant correlation between certain kinds of speech phenomena and brain lateralization. More precisely, on the basis of substantial neurolinguistic research it is argued that novel speech is represented in the left hemisphere, whereas formulaic speech is modulated by a subcortical right hemisphere circuit. Within the framework of Discourse Grammar (Heine et al. 2013) it is argued that there is a similar correlation between two domains of grammar, namely Sentence Grammar and Thetical Grammar: Aphasic patients and other persons with left hemisphere damage appear to draw mainly on linguistic expressions within the domain of Thetical Grammar; persons with right hemisphere damage, by contrast, use primarily Sentence Grammar as their main domain of structuring speech (Heine et al. 2014). While arriving at similar conclusions, there are a few differences between these two frameworks. In particular, the dual process model relies on the distinction between novel and formulaic speech as its main parameter, while in the framework of Discourse Grammar it is distinctions in the functions and the syntactic and prosodic independence of linguistic units that are most central. The present paper argues that such differences can be accounted for with reference to the differential role played by the situation of discourse in linguistic communication.