Abstract: Let G be a Lie group, S ? G a subsemigroup and G / H a homogeneous space of G. It is considered here the subsets of G / H, associated to the action of S, which corresponds to the chain control sets for control systems[1]. Their formal definition requires a family F of subsets of S. and when particularized to a control semigroup recovers its original form. lt is shown. under broad conditions, that a chain control set is the intersection of control sets for semigroups generated by the neighborhoods of the subsets in F. This fact permits to prove, for the chain control sets, results similar to those in [12] about control sets on the flag manifolds of semi-simlpe Lie groups Ver menos