In this chapter we study random walks on a finitely generated group G which has a free action on a Z(n)-tree. We show that if G is nonabelian and acts minimally, freely and without inversions on a locally finite Zn-tree Gamma with the set of open ends Ends(Gamma), then for every nondegenerate probability measure mu on G there exists a unique mu-stationary probability measure v(mu) on Ends(F), and the space (Ends(Gamma), v(mu)) is a mu-boundary. Moreover, if mu has finite first moment with respect to the word metric on G (induced by a finite generating set), then the measure space (Ends(Gamma), v mu) is isomorphic to the Poisson Furstenberg boundary of (G,mu).