  The high order corrections to renormalon are considered. Each new type of
insertions into the renormalon chain of graphs generates the correction to the
asymptotics of perturbation theory of the order of $\sim 1$. However, this
series of corrections to the asymptotics is not the asymptotic one (i.e. the
$m$-th correction does not grow like $m!$). The summation of these corrections
for UV renormalon may change the asymptotics by factor $N^\delta$. For the
traditional IR renormalon the $m$-th correction diverges like $(-2)^m$.
However, this divergency has no infrared origin and may be removed by proper
redefinition of IR renormalon. On the other hand for IR renormalons in hadronic
event shapes one should naturally expect these multi-loop contributions to
decrease like $(-2)^{-m}$. Some problems expected upon reaching the best
accuracy of perturbative QCD are also discussed.
