We search for lepton flavour violating events ($\rm e\mu$, $\rm e\tau$ and 
$\rm \mu\tau)$ that 
could be directly produced in $\rm e^+e^-$ annihilations, using 
the full available data sample collected with the 
OPAL detector at centre-of-mass energies between 
189 GeV and 209 GeV. 
In general, the 
Standard Model expectations describe the data well for all the
channels and at each $\rm \sqrt{s}.$ A single $\rm e\mu$
event is observed where according
to our Monte Carlo simulations only 0.019 events are
expected from Standard Model processes.
We obtain the first limits on 
the cross-sections $\rm \sigma(e^+e^-\rightarrow e\mu,\ e\tau\ and\ \mu\tau) $ 
as a function of $\rm \sqrt{s} $ at LEP2 energies.