The urgency of the study is due to the need to provide graduates of the Doctor of Philosophy educational and scientific programs with the mastery in methodology of pedagogical activities. The purpose of the article is to analyze the content, scope, components of the pedagogical component of educational and scientific programs aimed at training a Doctor of Philosophy. To achieve the purpose of the article we used these general scientific methods: analysis, synthesis, comparison, specification, generalization, content analysis to identify and characterize the peculiarities of developing the ability to teach students of the third (educational-scientific) level within the educational process of modern higher education institutions. The importance of the formation of teaching competence in the context of compliance with the provisions of legal documents related to the training of Doctors of Philosophy, descriptors of the National Qualifications Framework, criteria for assessing the quality of the educational program and professional standards is substantiated. It is emphasized that relevant competences, programme learning outcomes and educational components providing student’s development as a representative of academic staff are normative provisions of the programme under focus. It is emphasized that the formation of the pedagogical component of educational and scientific programs aimed at training a Doctor of Philosophy depends on the policy of an institution of higher education, which determines the scope of pedagogical (teaching) practice, sets disciplines prerequisites. Some possibilities of non-formal education for the development of the future PhD’s teaching competence are outlined. The conclusion about the role and importance of the pedagogical component of educational and scientific programs aimed at training a Doctor of Philosophy is made.