It is widely assumed that “And-But-Or” languages exploit a universal strategy for connecting phrasal coordinands due to the fact that coordination is considered basic and universal to the human mind and that the coordinators And and Or are equivalent to logical connectives. However, a contrastive study of Russian and Danish reveals significant differences between the two languages in the choice of the type of phrasal coordination in utterances used to describe one and the same type of situation. It appears that disjunction in Danish corresponds consistently to conjunction as well as disjunction in Russian, which cannot be accounted for by existing global formal semantic and pragmatic theo-ries. In this paper I propose a new approach to phrasal coordination in general and disjunction in particular based on Durst-Andersen’s cognitive-semiotic theory of linguistic supertypes, according to which Russian is a reality-oriented language with a third-person-oriented speaker and Danish is a hearer-oriented language with a second-person-oriented speaker. I claim that the use of disjunction and conjunction in these languages is determined by their essential properties as two different su-pertypes, viz. by the ground-situational nature of linguistic structures in Russian, the grammar of which functions as a model of situations in reality, and by the ground-propositional nature of lin-guistic structures in Danish, the grammar of which functions as a signal to the hearer to find situa-tions behind the speaker’s information.