  In their first article, the authors initiated a systematic study of
hyperbolic $\Lambda$-metric spaces, where $\Lambda$ is an ordered abelian
group, and groups acting on such spaces. The present paper concentrates on the
case $\Lambda = \mathbf{Z}^n$ taken with the right lexicographic order and
studies the structure of finitely generated groups acting on hyperbolic
$\mathbf{Z}^n$-metric spaces. Under certain constraints, the structure of such
groups is described in terms of a {\em hierarchy} similar to the one
established for $\mathbf{Z}^n$-free groups by Kharlampovich, Myasnikov,
Remeslennikov and Serbin.
