  We study the statistics of encounters of L\'evy flights by introducing the
concept of vicious L\'evy flights - distinct groups of walkers performing
independent L\'evy flights with the process terminating upon the first
encounter between walkers of different groups. We show that the probability
that the process survives up to time $t$ decays as $t^{-\alpha}$ at late times.
We compute $\alpha$ up to the second order in $\epsilon$-expansion, where
$\epsilon=\sigma-d$, $\sigma$ is the L\'evy exponent and $d$ is the spatial
dimension. For $d=\sigma$, we find the exponent of the logarithmic decay
exactly. Theoretical values of the exponents are confirmed by numerical
simulations.
