  In this paper we generalize the notion of strongly poly-free group to a
larger class of groups, we call them strongly poly-surface groups and prove
that the Fibered Isomorphism Conjecture of Farrell and Jones corresponding to
the stable topological pseudoisotopy functor is true for any virtually strongly
poly-surface group. A consequence is that the Whitehead group of a torsion free
subgroup of any virtually strongly poly-surface group vanishes.
