The paper presents the approach to competences in the context of the problem of the distance learning process. The place of the problem of determining competence in ODL is analyzed. Competence in ODL conditions is becoming one of the basic instruments for assessing the quality of the learning process. Therefore, it is important to develop the theoretical basis for modeling competences and adapt this model to practical needs. An approach combining methods of game theory and fuzzy sets would allow determining the degree of competence possessed and acquired by all participants in the teaching process. In the paper the new educational model developed on acquiring the project team competence is represented. The issue of selecting partners to work on the project profile is being considered. The quality of the project team is determined by the degree of coverage of the domain of the project profile by the competences of its participants.