  For a group G that splits as an amalgamation of A and B over a common
subgroup C, there is an associated Waldhausen Nil-group, measuring the
"failure" of Mayer-Vietoris for algebraic K-theory. Assume that (1) the
amalgamation is acylindrical, and (2) the groups A,B,G satisfy the
Farrell-Jones isomorphism conjecture. Then we show that the Waldhausen
Nil-group splits as a direct sum of Nil-groups associated to certain
(explicitly describable) infinite virtually cyclic subgroups of G. We note that
a special case of an acylindrical amalgamation includes any amalgamation over a
finite group C.
