With Kazakhstan's accession to the Bologna Process, particular importance is attached to the professionally-oriented approach of teaching foreign languages to students, which facilitates formation of their foreign language communicative ability. The article deals with the problem of teaching English to students for the purpose of formation of international communicative competence of the future experts with the aid of professional discourse, which is defined as a verbal communication aimed at solving theoretical and practical problems that requires training and experience in a definite sphere of activity. The paper considers "discourse" from the perspectives of different theories and authors, it describes the main characteristics and types of discourse, differentiated the terms "discourse" and the term "text," examined the peculiarities of them and it also lists specific features of "discursive competence" and accentuates its importance in the process of teaching foreign language communication within the new paradigm of Kazakh education system.