We have searched for lepton flavour violation in Z boson decays into l
epton pairs using all data collected with the L3 detector during the 1
990, 1991 and 1992 runs on an event sample corresponding to 1 500 000
Z's produced. At the 95% confidence level the upper limits on the bran
ching ratio for Z --> emu is 0.6 x 10(-5), for Z --> etau this is 1.3
x 10(-5) and for Z-mutau this is 1.9 X 10(-5).