Subject matter of the research: cognitive communicative discourse properties of a bilingual. The objective was to characterize a bilingual’s capacities of forming the types of knowledge and skills during several stages of formation of his/her competence. Methodology: in the article there were used as a methodological basis the cognitive and anthropocentric principles, competence approach, focusing on the study of the ways of formation and representation of knowledge, skills, and competencies of man in his cognitive activity. Methods of work: a conceptual analysis, dialingual analysis (identification and description of the types of interference), the competence analysis, discourse method. Results: 1) the author studied the bilingual personality as one of the types of language personality; 2) the author described in a cognitive aspect types of knowledge a bilingual acquires at various stages of formation of his/her competence; 3) identified the types of knowledge phonetic, lexical, grammatical (linguistic) and cultural at the first and second stages of a bilingual’s competence formation arising from a personality’s insufficient competence in the second language and culture of the nation of the target language; 4) clarified a bilingual’s cases of misunderstandings the connotative meanings of words and idioms in the second language; 5) proved the necessity of forming the communicative pragmatic competence, recognizing the speakers’ intentions, for regulating the communication. In conclusion it should be noted that the issue of competence building of a bilingual in the second language is one of the problems that is not completely solved. The main way to solve this issue is to take into account the need to master not only the knowledge (cognitive aspect), but discursive properties of a speech in the second language (knowledge of the speaker’s intentions, mastering the pragmatic norms, pragmatic value, the ability to model frames, to conceptualize the notion (cognitive and discursive aspects).