We consider a Λ-coalescent and we study the asymptotic behavior of
the total length Lext(n) of the external branches of the associated
n-coalescent. For Kingman coalescent, i.e. Λ=δ0, the result
is well known and is useful, together with the total length L(n), for Fu
and Li's test of neutrality of mutations% under the infinite sites model
asumption . For a large family of measures Λ, including
Beta(2−α,α) with 0<α<1, M{\"o}hle has proved asymptotics
of Lext(n). Here we consider the case when the measure Λ is
Beta(2−α,α), with 1<α<2. We prove that
nα−2Lext(n) converges in L2 to
α(α−1)Γ(α). As a consequence, we get that
Lext(n)/L(n) converges in probability to 2−α. To prove the
asymptotics of Lext(n), we use a recursive construction of the
n-coalescent by adding individuals one by one. Asymptotics of the
distribution of d normalized external branch lengths and a related moment
result are also given