Awareness of competence and structured competence representations are important elements in different business scenarios such as a company looking for a partner with expertise in a certain industrial sector or new staff member with particular skills. This paper presents the use of ontologies to formally represent competence models describing individual and enterprise competences. The individual competences model includes the three major parts: general competence, cultural competence, and occupational competence. The enterprise competences model consists of two parts: industrial competence and occupational competence. The competence models are defined with a meta-model, the latter being an ontology language. Particular individuals and enterprises are described with competence profiles, which are instances of the models. During a pilot study, five individual competence profiles and four enterprise competence profiles were built. The approach to competence modeling has proved to be able to capture capabilities of individuals with diverse occupational and educational backgrounds. Furthermore, the competence modeling approach proved to be suitable for enterprise competences in different countries due to use of international standard classifications as a basis of the models.