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.Facultad de Ciencias Exactas