The article is focused on the organization of global and local structures of modern Russian legal discourse. Discursive fragments of defensive and accusatory speeches of modern forensic orators are examined in the scope of the Rhetorical structure theory, diagrams of their rhetorical structures are modeled, and the specifics of interaction between discursive units are explored. The goal of scientific analysis is to establish cognitive and rhetorical factors in the organization of discursive fragments of modern linguistic legal communication of persuasive type. The goal is achieved using general scientific and linguistic methods proper, including the method of formalizing linguistic descriptions: constructing tree-like diagrams of rhetorical structures related to the discourse fragments and a diagram of the cognitive profiling mechanism. The rhetorical aspect of scientific research reveals itself in identifying areas for actualization of the pragmatic layer of the semantics of text units and ways of its expression by means of the Russian language; establishing functionally significant aspects of the interaction between the informative and pragmatic layers of the semantics of text units. The study revealed the specifics of the organization of the global structure of legal discourse, its subordination to the original communicative intention, and established its correlations with types of rhetorical links that organize discursive fragments. The authors identify and give grounds to the most frequent rhetorical relations of a presentational type, aimed at strengthening the illocutionary profile of a text unit, and rhetorical relations of a denotative nature, correlating with logical-semantic relations between discursive units. It has been established that the initial communicative intention is supported by more specific propositional attitudes and together they form an intentional complex that determines the rhetorical structure of the discourse as a whole.