In this paper an extensive study of the concepts of generalized Green's relations and GV-semigroups without order to ordered semigroups have been given. Our approach allows one to see the nature of generalized Green's relations in the class of GV-ordered semigroups. Moreover we show that an ordered semigroup S is a GV-ordered semigroup if and only if S is a complete semilattice of completely π-regular and Archimedean ordered semigroups.