  For $1<\alpha <2$ we derive the asymptotic distribution of the total length
of {\em external} branches of a Beta$(2-\alpha, \alpha)$-coalescent as the
number $n$ of leaves becomes large. It turns out the fluctuations of the
external branch length follow those of $\tau_n^{2-\alpha}$ over the entire
parameter regime, where $\tau_n$ denotes the random number of coalescences that
bring the $n$ lineages down to one. This is in contrast to the fluctuation
behavior of the total branch length, which exhibits a transition at $\alpha_0 =
(1+\sqrt 5)/2$.
