  We consider Beta$(2-\alpha, \alpha)$-coalescents with parameter range $1
<\alpha<2$ starting from $n$ leaves. The length $\ell^{(n)}_r$ of order $r$ in
the $n$-Beta$(2-\alpha, \alpha)$-coalescent tree is defined as the sum of the
lengths of all branches that carry a subtree with $r$ leaves. We show that for
any $s \in \mathbb N$ the vector of suitably centered and rescaled lengths of
orders $1\le r \le s$ converges in distribution to a multivariate stable
distribution as the number of leaves tends to infinity.
