The article deals with the research methods of a discourse – Discourse Analysis and Critical Discourse Analysis. With the appearance of a new term ‘‘discourse’’, methods of its research started to be worked out by different scholars. The author states that within 20-25 years a semantic meaning of ‘‘discourse’’ has changed. The article analyses these changes and gives the main interpretations of ‘‘discourse’’, stressing that the basis for understanding of ‘‘discourse’ was established by a famous scholar T.A. van Dijk. Theoretical works by T.A. van Dijk stimulated further research of discourse and broadening of its interpretation. Nowadays discourse is interpreted not only as a structure but also as a process. Discourse Analysis and Critical Discourse Analysis are two most popular methods of discourse research. Discourse Analysis arises from linguistic. It focuses on the research of texts in a social context. Discourse Analysis studies the language in a certain situation and in a certain field. In Discourse Analysis the language functions not as a structure but as a content of different social practices. Critical Discourse Analysis is characterized by its constructive problem-oriented interdisciplinary approach. Critical Discourse Analysis differs from Discourse Analysis in: the nature of problems discussed; the choice of research objects; the relations between language and society (which are here viewed as intermediary); the statement that discourse can be interpreted only in its context; the predominance of socio-cognitive aspects over linguistic ones. Summarizing the postulates of Discourse Analysis and Critical Discourse Analysis the author comes to the conclusion that for a detailed research of media discourse it is necessary to apply a synthesis of both methods as each method alone appears to be somehow limited. On the basis of Discourse Analysis and Critical Discourse Analysis the author defines six points for media discourse analysis. Key words: discourse, media discourse, discourse analysis, critical discourse analysis.