Under discussion is the management of long-lived high-level wastes in the nuclear energy sector of Russia, the development of which on a large scale in the next century is motivated by the need for arresting the increasing consumption of fossil fuels. The prerequisites for the nuclear power growth consists in the design of naturally safe reactors and development of a transmutational nuclear fuel cycle (NFC) technology. The choice of operations in such a cycle and of their quantitative characteristics, is aimed at minimizing the wastes to approach the radiation balance with the natural uranium extracted and put to use. The paper discusses the way the approximation to the balance between the raw material and waste activity is influenced by introduction of the transmutational NFC (in case 2), inclusion of transmutation reactors into the energy mix (case 1), partial disposal of actinide wastes into outer space, and by recycling of protactinium (case 3). It is shown that such a balance can be sustained for a considerable time in cases 2 and 3 or throughout the operation stage of the future nuclear power (case 1).