The article based on the analysis of scientific publications identifies three approaches to understand the structure of competence as a matter of assessment. The authors reveal the main problems faced by university teachers in the evaluation of competencies (substitution of the subject assessment, identification of correspondence between specific topics of discipline and competence components; harmonization of teachers of different disciplines in the process of formation and evaluation of competences and others). The article shows the role and place of different means of diagnosis and assessment of competencies; tendencies of the development of forms and methods for assessing competencies. Taking into account the prolonged character of assessment process it is expedient to use individual diagnostic cards that enable to register all the stages of competence components formation and thus to get the dynamic competence model. This approach is efficient in regard to non-cognitive competence components (motivation, value, activity). It also implies using the model of concentrated education (three-four courses with interdisciplinary ties in a module, three-four modules within a semester). The authors come to a conclusion of a necessity to implement competency-oriented assessment tasks in every training area and in every course.