%0 Journal Article %T The "fundamental theorem" for the algebraic K-theory of spaces. III. the nil-term %A John R. Klein %A Edward Bruce Williams %J Mathematics %D 2007 %I arXiv %X In this paper we identify the ``nil-terms'' for Waldhausen's algebraic K-theory of spaces functor as the reduced K-theory of a category of equivariant spaces equipped with a homotopically nilpotent endomorphism. %U http://arxiv.org/abs/0705.0930v2