This article is devoted to the problem of social competences training with opportunities for graduates to adapt to current labor market challenges. In the article the author presents several definitions of the “competence” notion, reproduces categories of competences (basic competences, key-competences, competences for employment, entrepreneurial competences, managerial competences, competences for life, social and civic competences); presents the definition of social competences and reveals the necessity of their training (among university graduates) in employment brink; proposes social competences training strategies in university education; analyzes the results of a survey regarding the knowledge of social competences among students and the necessity of their training.