Аннотация:A search for the lepton-flavour violating decays B0→K∗0μ±e∓ and B0s→ϕμ±e∓ is presented, using proton-proton collision data collected by the LHCb detector at the LHC, corresponding to an integrated luminosity of 9fb−1. No significant signals are observed and upper limits ofB(B0→K∗0μ+e−)B(B0→K∗0μ−e+)B(B0→K∗0μ±e∓)B(B0s→ϕμ±e∓)<5.7×10−9 (6.9×10−9),<6.8×10−9 (7.9×10−9),<10.1×10−9 (11.7×10−9),<16.0×10−9 (19.8×10−9)are set at 90% (95%) confidence level. These results constitute the world's most stringent limits to date, with the limit on the decay B0s→ϕμ±e∓ the first being set. In addition, limits are reported for scalar and left-handed lepton-flavour violating New Physics scenarios.