search for lepton flavour number violating Z0 decays in the channels Z0 --> µt, Z0 --> et , Z0 --> eµ, using the DELPHI detector with data collected during the 1991–94 LEP runs, is described. No signal was found. Upper limits at 95% confidence level for the respective branching fractions of 1.2 x 10−5, 2.2 x 10−5, and 0.25 x 10−5, were obtained.