A cascade subcritical liquid-salt reactor designed for burning long-lived components of the radioactive wastes of the nuclear fuel cycle is examined. The cascade scheme of the reactor makes it possible to decrease by a factor of three the power of the driving accelerator as compared with conventional accelerator-blanket systems of equal power. The fuel composition of the reactor consists of 20% Np, Am, Cm, and other transplutonium elements and 80% plutonium, which are dissolved in a salt melt NaF(50%)-ZrF 4 (50%). For a 10 MW proton accelerator, 1 GeV proton energy (10 mA current) and subcriticality depth 0.05, the thermal power of the reactor is 800 MW, which permits burning ~70 kg/yr Np, Am, Cm, and other transplutonium actinides, i.e., service five VVÉR type reactors of equal power.The problem of handling radioactive nuclear wastes from nuclear power generation remains unsolved even at the strategic level. The only solution which has reached commercial implementation -burial in deep geological formationsis being challenged today [1]. Another (strategically more natural) solution to this problem -burning (transmutation) in fast reactors -can be implemented only after most of the thermal reactors are replaced by fast reactors, and it requires a long period of time [2]. The third route -the development of special burner reactors -has been under intense discussion in recent years but is still at the conceptual stage. The main difficulty of developing such reactors is the low fraction of delayed neutrons (β = 0.17%) with fissioning of Np, Am, Cm, and other transplutonium actinides, which makes it impossible to construct high-capacity and safe critical burner reactors, since the admissible fraction of the actinides in the fuel of such reactors does not exceed 3-5% [3,4]. Switching to subcritical systems with k eff < 1 eliminates this difficulty but requires an intense source of neutrons. In accelerator-blanket systems, the neutrons produced by a beam of accelerated charged particles (electrons, protons, deuterons) in a heavy target is such a source. Specifically, each proton with energy E ≈ 1 GeV creates ~20 neutrons in a lead target. The thermal power of the blanket (W b ) and the power of the driving accelerator (W a ) are related by the relation [5]