The paper consists of five parts.Part one is devoted to the definition of the most important concept of the competence approach - the competence. The overwhelming majority of numerous papers, concerning the education system is based on some incorrect definition of this concept. The second part contains “General requirements to formation of essential competences, concerning an object of research”, i. e. a major issue of research, a definite didactic subject, a discipline etc. Part Threepresents a technique of forming the essential competences and, further, the competencies on their basis. The competencies are created taking into account the fundamental terms of concrete subjects or disciplines. The fourth part describes the organization principles of education systems considering the human factor. Finally, the fifthpart consists of two types of models: the first type contains two models of forming the essential competence concerning a concrete subject (discipline), and the second type describes two models of increasing the competence in a discipline as a whole.