The talk is about the construction of stable pseudoisotopy spaces as a functor on the category of manifolds (with continuous maps as morphisms). I will then formulate a Farrell-Jones-Conjecture for this pseudoisotopy functor. If time permits, I will also give a short status report on an ongoing research project with Wolfgang Lück, Malte Pieper, Mark Ullmann and Christoph Winges about proof for the Farrell-Jones-Conjecture for pseudoisotopy- and A-theory.