The research addresses the particular features of CLIL approach used at tertiary level. The main focus is done on the necessity to educate teachers, who are involved in CLIL teaching. Despite the fact that CLIL with the embedded methodologies has been used relatively for a long time in Russian universities, there is still no a common understanding among both administration and teaching staff on how it should be used correctly and what resources are needed for it. All these conclusions the authors of the paper came after a long pedagogical observation, practices, surveys and polls among students and teachers. Based on the experimental data, the authors made a conclusion that universities have to work out a firm and clear conception regarding to what CLIL is, how CLIL-courses should be planned and taught, what resources, human and material, it will require. Among material and human resources, the authors choose the latter because if a teacher knows what to do, what the goal of the teaching is and what results are expected, material resources stop being a problem. The authors propose such a term as CLIL-competence that will be included in the common portrait of a subject-teacher qualification and allow to fulfill the stated goal at more efficient level. However, the analysis of documents has shown that neither Russian pedagogical university in its programs contains anything concerning the readiness for teachers to work effectively under subjectlanguage collaboration. The authors assume that this statement can be debated among practitioners and researchers. The debates can relate to the fact that the regulating documentation contain the competences allowing teachers to work in international academic and professional environments, as well, it contains the competences including the knowledge how to work with modern educational technologies and methods. The authors, nevertheless, suggest that the CLIL-competence has a particular set of knowledge and skills subordinated to the common pedagogical competences but with its specific content. The literature analysis allowed the authors to find only two documents recognized in the world, which present the CLIL descriptors. These documents are 1) CLIL Teacher's Competences Grid and 2) EFFCTE. Both documents include approximately the same set of competences but the principles these documents are composed are different. The authors of the paper developed own criteria to assess the CLIL-competence of university teachers in Russia. The assessment was organized in two steps with two different instruments. The data were collected through two surveys, where one was based on self-assessment of the respondents. As quantitative indicators, the average number was calculated that was equal to 2.8 indicating the critical threshold. The results showed that only three indicators exceeded the critical red line and appeared in a zone of the positive growth. To such indicators are referred the follows: students' support when choosing optimal learning tools and methods, collaboration with colleagues, a help to students in understanding their needs in CLIL- courses. Some indicators appeared significantly low the red line, among them: understanding the ration between the goal and learning outcomes, the choice of assessment tools and materials considering language difficulties and its non-homogenous level of students. The questions relating to the assessment of the common level of teaching competences - the ability to select the content for CLIL-courses, select appropriate exercises, do a good planning - showed the level that was lower the red line. This demonstrates, in the authors' opinion, the level of uncertainty among the respondents when they work with the CLIL-tools. In general, the experiment allowed to identify and describe some weak sides existing currently in CLIL teaching and, as a consequence, propose some solutions targeted at their elimination