Didactic aspects of the educational component of doctoral training appear highly significant for modern doctoral education. The educational component involves two parts: research and teaching training. The dual nature of training, which includes different and, at the same time, interrelated types of learning activities, requires the development of appropriate research and methodological support of doctoral education. The methodological basis of designing and implementation of the educational component of doctoral training at an engineering university is an integrated approach. A comprehensive system of training is based on the combining of learning material in a certain semantic environment. This semantic environment is represented by the personal development of PhD students, along with the development of her/his professional mobility, competence, increasing competitiveness and improving the quality of training. The processes of designing and implementation of the educational component entail the use of a systematic approach, whereby the designed objects (preparation for the research along with the preparation for teaching activities) are considered as separate pedagogical systems; competence and activity approaches aimed at the development of general and professional competencies within research and teaching activities; personality-oriented approach focused on the educational component for personal development of PhD students within the research and teaching activities in accordance with their individual curricula. The authors discuss the elements of the pedagogical model of PhD students training at engineering universities.