We have searched for lepton flavour violation in Z0 boson decays into lepton pairs, Z0→μτ, Z0→eτ, and Z0→eμ. The data sample is based on an integrated luminosity of 10.4 pb-1 corresponding to 370 000 Z0’s produced. We obtain upper limits on the branching ratios of 4.8 X 10-5 for the μτ 3.4 X 10-5 for the eτ and 2.4 X 10-5 for the eμ decay modes at the 95% confidence level.