  In this paper, we study the action of non abelian group G generated by affine
homotheties on R^n. We prove that G satisfies one of the following properties:
(i) there exist a subgroup F_{G} of R\{0} containing 0 in its closure, a
G-invariant affine subspace E_{G} of R^n and a in E_{G} such that for every x
in R^n the closure of the orbit G(x) is equal to F_{G} .(x - a) +E_{G}. In
particular, G(x) is dense in E_{G} for every x in E_{G} and every orbit of U =
R^n\E_{G} is minimal in U. (ii) there exists a closed subgroup H_{G} of R^n and
a in R^n such that for every x in R^n, the closure of the orbit G(x) is equal
to the union of (x + H_{G}) and (-x + a + H_{G}).
