Actions of locally nilpotent groups on Lambda-trees

For certain classes of groups, it is shown that there are restrictions on t he type of action a group in the class can have on a Lambda-tree, where Lam bda is an arbitrary ordered abelian group, generalizing results by other au thors in the case Lambda = R. The main classes considered are locally nilpo tent, polycyclic by finite, locally (polycyclic by finite) and locally (hyp erabelian by finite). The arguments involve an investigation of the relatio n between the type of action a group has on a Lambda-tree and the type of a ction of its subgroups by restriction.