The distance education system is actively developing in the world due to the COVID-19 pandemic. The sharp transition of PhD candidates to distance education caused difficulties in organising the educational process. The aim of this study was to analyse the methods of distance education for postgraduate students in the context of a COVID-19 pandemic. A survey of graduate students was conducted through specially-designed and semi-standardised interviews of focus groups of producers and consumers of educational services. The study showed that the process of adaptation of postgraduate students majoring in Physical Culture and Sports and Biology was much more difficult than in the major Educational, Pedagogical Sciences and Philology. The reasons for the problems of distance education of PhD candidates included the complexity of creating educational and methodological materials for distance learning; lack of a centralised system of certification and accreditation of electronic courses; insufficient motivation of teachers; shortage of teachers who could competently develop distance learning courses in higher education. The study identified opportunities to implement promising areas of online learning in the system of training of academic and teaching staff: retraining of a large proportion of the teaching staff, implementation of a system approach to the development of the online environment of educational institutions, development of skills and abilities to use educational content. Prospects for further research include the study of problems of violation of academic integrity by postgraduate students in the course of distance learning.