A search for lepton flavour violation through the decays Z0 → eμ, eτ and μτ was made with the DELPHI detector at LEP, using a sample corresponding to an integrated luminosity of 11.2 pb−1. The number of candidates was consistent with the estimated background. The upper limit on the branching ratio (at 95% confidence level) forZ0 → eμ was 3.2 × 10−5, for Z0 → eτ was 10.8 × 10−5 and for Z0 → μτ was 13.5 × 10−5.