  Let $M$ be a finite dimensional topological aspherical manifold whose
universal cover is ${\bf R}^n$. In this paper, we study $Aff(M)$, the subgroup
of the group of homeomorphisms of $M$, whose elements can be lifted to affine
transformations of ${\bf R}^n$. We show that if $M$ is closed, the connected
component $Aff(M)_0$ of $Aff(M)$ acts locally freely on $M$. We deduce that
$Aff(M)_0$ is a solvable Lie group, and is nilpotent if $M$ is a polynomial
manifold. We study the foliation defined by the orbits of $Aff(M)_0$ if
$dim(Aff(M)_0)=dim(M)-1$.
