We have searched for lepton flavour violation in Z boson decays into lepton pairs using all data collected with the L3 detector during the 1990, 1991 and 1992 runs on an event sample corresponding to 1 500 000 2?s produced. At the 95% confidence level the upper limits on the branching ratio for Z--,etz is 0.6X 10 -s, for Z--.er this is 1.3X 10 -5 and for Z--*/zT this is 1.9X 10 -s.Facultad de Ciencias Exactas