A search for the lepton-flavour violating decays B 0 → K *0 μ ± e ∓ and Bs0 → ϕμ ± e ∓ is presented, using proton-proton collision data collected by the LHCb detector at the LHC, corresponding to an integrated luminosity of 9 fb −1. No significant signals are observed and upper limits of B(B0→K∗0μ+e−)<5.7×10−9(6.9×10−9),B(B0→K∗0μ−e+)<6.8×10−9(7.9×10−9),B(B0→K∗0μ±e∓)<10.1×10−9(11.7×10−9),B(Bs0→ϕμ±e∓)<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 Bs0 → ϕμ ± e ∓ the first being set. In addition, limits are reported for scalar and left-handed lepton-flavour violating New Physics scenarios. [Figure not available: see fulltext.].