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In this paper, we consider Beta$(2-{\alpha},{\alpha})$ (with $1<{\alpha}<2$)and related ${\Lambda}$-coalescents. If $T^{(n)}$ denotes the length of anexternal branch of the $n$-coalescent, we prove the convergence of$n^{{\alpha}-1}T^{(n)}$ when $n$ tends to $ \infty $, and give the limit. Tothis aim, we give asymptotics for the number $\sigma^{(n)}$ of collisions whichoccur in the $n$-coalescent until the end of the chosen external branch, andfor the block counting process associated with the $n$-coalescent.

On the length of an external branch in the Beta-coalescent