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Nuclear decays with simultaneous emission of two alpha particles are energetically possible for a number of nuclides. Prospects of searching for such kind of decay for nuclides present in the natural isotopic composition of elements are discussed here. The first experimental limit on half-life for 2α decay is set for 209Bi as T1/2 > 2.9·1020 y at 90 % C.L., using the data of work [P. de Marcillac et al. Nature 422 (2003) 876]. Theoretical T1/2 estimations for the process are also given. Using these values, which are on the level of 1033 y or more, one can conclude that the prospects of experimental observation of 2α decay are very pessimistic.