  Groups acting freely on Z^n-trees (Z^n-free groups) play a key role in the
study of non-archimedean group actions. Following Stallings' ideas, we develop
graph-theoretic techniques to investigate subgroup structure of Z^n-free
groups. As an immediate application of the presented method, we give an
effective solution to the Uniform Membership Problem and the Power Problem in
Z^n-free groups.
