Abstract: A search for the lepton-flavour violating decays B-(s)(0) -> e(+/-)mu(-/+) and B-(s)(0) -> e(+/-)mu(-/+) performed based on a sample of proton-proton collision data corresponding to an integrated luminosity of 3 fb(-1), collected with the LHCb experiment at centre-of-mass energies of 7 and 8TeV. The observed yields are consistent with the background-only hypothesis. Upper limits on the branching fraction of the B-(s)(0) -> e(+/-)mu(-/+) decays are evaluated both in the hypotheses of an amplitude completely dominated by the heavy eigenstate and by the light eigenstate. The results are B(B-s(0) -> e(+/-)mu(-/+)) < 6.3 (5.4) x 10(-9) and B(B-s(0) -> e(+/-)mu(-/+)) < 7.2(6.0) x 10(-9) at 95% (90%) confidence level, respectively. The upper limit on the branching fraction of the B-0 -> e(+/-)mu(-/+) decay is also evaluated, obtaining B(B-0 -> e(+/-)mu(-/+)) < 1.3 (1.0) x 10(-9) at 95% (90%) confidence level. These are the strongest limits on these decays to date.