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A search for the decays Bs0 → e+e− and B0 → e+e− is performed using data collected with the LHCb experiment in proton-proton collisions at center-of-mass energies of 7, 8, and 13 TeV, corresponding to integrated luminosities of 1, 2, and 2 fb − 1 , respectively. No signal is observed. Assuming no contribution from B0 → e+e− decays, an upper limit on the branching fraction B (Bs0 → e+e−) < 9.4 ( 11.2 ) × 10−9 is obtained at 90(95)% confidence level. If no Bs0 → e+e− contribution is assumed, a limit of B (B0 → e+e−) < 2.5 ( 3.0 ) × 10−9 is determined at 90(95)% confidence level. These upper limits are more than one order of magnitude lower than the previous