We search for lepton flavour violating events (e mu, e tau and mu tau) that
could be directly produced in e(+) e(-) annihilations, using the full avai
lable data sample collected with the OPAL detector at centre-of-mass energi
es between 189 GeV and 209 GeV. In general, the Standard Model expectations
describe the data well for all the channels and at each roots. A single et
t event is observed where according to our Monte Carlo simulations only 0.0
19 events are expected from Standard Model processes. We obtain the first l
imits on the cross-sections sigma (e(+)e(-) --> e mu, e tau and mu tau) as
a function of roots at LEP2 energies. (C) 2001 Elsevier Science B.V. All ri
ghts reserved.