Abstract: A radiocactive waste containing medium is circulated within two or more systems (1,2,3) separated from each other flowtechnically; and the circulated radioactive waste is exposed to neutron radiations of different energy spectrum in each system by operating a reactor physically united entirety of irradiated sections of the said systems as a nuclear reactor or an accelerator driven subcritical system. Each system (1,2,3) has a heat exchanger (9,10) and, in given cases, a circulating pump (10,21) and an expansion tank (5,16,27). The disclosed apparatus has two or more reactor regions (1,2,3) separated from each other by partitions (37,38) and, preferably, arranged coaxially within a reactor space encircled by a common shell structure (39). A particle beam (45) produced by a particle accelerator is preferably directed into the innermost reactor region (3).