The investigation gives the author’s view on teaching creative translation by researching the case of the cognitive political discourse analysis procedure. Of a particular interest is the fact that the research material is based on the example of the discourse analysis of modern political terminology and other non-equivalent vocabulary within the bounds of political contexts. Unlike traditional approaches connecting creativity to literary texts studies, the paper deals with the methodology of comprehending and translating foreign academic and scientific texts. The cognitive study of contextual actualization of political concepts in the English and Russian discourses through their comparative analysis is aimed at professional explanation of motivation in choosing translation equivalents. The algorithm of making up an associative thesaurus based on cognitive signs of lexical marking has been used as the major tool of political discourse analysis as well as the foundation for the original creative model of teaching translation.