Let $GA$ be the group of orientation preserving affine transformations on the real line. In 1980's, E.Ghys proved that if a smooth and locally free action of $GA$ on a closed three-manifold preserves a continuous volume, then it is smoothly conjugate to a classical homogeneous action. Many authors generalized Ghys's result to codimension-one volume preserving actions of higher dimensional solvable groups. It is natural to ask whether the assumption on an invariant volume is necessary or not. Recently, M. Belliart showed that it is not necessary for a large class of higher dimensional groups. However, the same question was open for $GA$. In this talk, I will give a classification of smooth and locally free actions of $GA$ on closed three-manifolds up to smooth conjugacy. As an immediate corollary, we will see that $GA$ admits non-homogeneous actions if the manifold is neither solvable nor a rational homology sphere. (Details are given in arXiv:math.DS/0702833)