Class-preserving automorphisms and inner automorphisms of certain tree products of groups

In general, a class-preserving automorphism of generalized free products of nilpotent groups need not be an inner automorphism. We prove that every class-preserving automorphism of tree products of finitely generated nilpotent or free groups, amalgamating infinite cyclic subgroups, is inner. It follows that the outer automorphism groups of such tree products, amalgamating infinite cyclic subgroups, are residually finite.