Аннотация:A first search for the lepton-flavour violating decays B0→K∗0τ±μ∓ is presented. The analysis is performed using a sample of proton-proton collision data, collected with the LHCb detector at centre-of-mass energies of 7, 8 and 13 TeV between 2011 and 2018, corresponding to an integrated luminosity of 9 fb−1. No significant signal is observed, and upper limits on the branching fractions are determined to be B(B0→K∗0τ+μ−)<1.0 (1.2)×10−5 and B(B0→K∗0τ−μ+)<8.2 (9.8)×10−6 at the 90% (95%) confidence level.