  We prove an acylindrical accessibility theorem for finitely generated groups
acting on $\mathbf R$-trees. Namely, we show that if $G$ is a freely
indecomposable non-cyclic $k$-generated group acting minimally and
$M$-acylindrically on an $\mathbf R$-tree $X$ then for any $\epsilon>0$ there
is a finite subtree $Y_{\epsilon}\subseteq X$ of measure at most
$2M(k-1)+\epsilon$ such that $GY_{\epsilon}=X$. This generalizes theorems of
Z.Sela and T.Delzant about actions on simplicial trees.
