  We introduce properties of metric spaces and, specifically, finitely
generated groups with word metrics which we call coarse coherence and coarse
regular coherence. They are geometric counterparts of the classical algebraic
notion of coherence and the regular coherence property of groups defined and
studied by F. Waldhausen. The new properties can be defined in the general
context of coarse metric geometry and are coarse invariants. In particular,
they are quasi-isometry invariants of spaces and groups. We show that coarse
regular coherence implies weak regular coherence, a weakening of regular
coherence by G. Carlsson and the first author. The latter was introduced with
the same goal as Waldhausen's, in order to perform computations of algebraic
K-theory of group rings. However, all groups known to be weakly regular
coherent are also coarsely regular coherent. The new framework allows us to
prove structural results by developing permanence properties, including the
particularly important fibering permanence property, for coarse regular
coherence.
