  We consider groups of automorphisms of locally finite trees, and give
conditions on its subgroups that imply that they are not elementary amenable.
This covers all known examples of groups that are not elementary amenable and
act on the trees: groups of intermediate growths and Basilica group, by giving
a more straightforward proof. Moreover, we deduce that all finitely generated
branch groups are not elementary amenable, which was conjectured by Grigorchuk.
