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Possibilities to search for double beta decay of alpha/beta unstable nuclei,many of which have higher energy release than "conventional" (beta stable)double beta decay candidates, are discussed. First experimental half-lifelimits on double beta decay of radioactive nuclides from U and Th families(trace contaminants of the CaWO_4, CdWO_4 and Gd_2SiO_5 scintillators) wereestablished by reanalyzing the data of low-background measurements in theSolotvina Underground Laboratory with these detectors (1734 h with CaWO_4,13316 h with CdWO_4, and 13949 h with Gd_2SiO_5 crystals).Comment: 15 pages, 6 figure

On the possibility to search for 2β decay of initially unstable (α/β radioactive) nuclei