Problems related to doctoral training are discussed, which is a priority function for European universities. It's shown that organization of doctoral programs varies by country and by university as well, that there exist two approaches to organization of doctoral training in European countries (individual programs and structural programs), that methods and forms of doctoral training vary depending on the significance assigned to individual research and the role of scientific supervisor. New problems and challenges faced by European universities in organizing doctoral training are emphasized, and tendencies affecting the training are shown by use of rich statistical data and evidence. It is concluded that the variety of traditions and approaches to organization of doctoral programs can be regarded as an advantage of the European Education Area, but also as a factor of fragmentation of doctoral training, not favorable for fostering a good research environment. Results of the project of the European Association of Universities (EAU) 'Doctoral Programs for the European Knowledge Society', ten basic principles for organization of doctoral training, fixed by the Salzburg scientific seminar and 'Dublin Descriptors' approved by the Bergen conference of ministers of higher education from Bologna process member states are reviewed. It's concluded that the EAU policy seeks to preserve the variety of doctoral training systems, so, introduction of a standard 'Eurodoctoral' degree shouldn't be expected in the near future.