We have searched for lepton flavour violating Z(0) --> e mu, Z(0) -->
e tau and Z(0) --> mu tau decays in a sample of 4.0 x 10(6) visible Z(
0) decays collected with the OPAL detector at LEP during 1991 to 1994.
No candidates are found for Z(0) --> e mu. The samples of selected Z(
0) --> e tau and Z(0) --> mu tau candidates are consistent with the ex
pected background. The following limits are set at 95% confidence leve
l: BR(Z(0) --> e mu) < 1.7 x 10(-6) BR(Z(0) --> e tau) < 9.8 x 10(-6)
BR(Z(0) --> mu tau) < 17. x 10(-6).