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Introduction. Suppose that G is an analytic subgroup and S is a subgroup of G. S is called a uniform subgroup of G if G/S is compact. S is called a full subgroup of G if the only analytic subgroup of G that contains S is G itself. The notion of full subgroup is first brought up by G. D. Mostow (131). Full subgroups of exponential groups (a simply connected solvable analytic group is said to be exponential if its exponential map is bijective) have been studied by the authors ([2]). It is the aim of this paper to study full subgroups of simply connected solvable analytic groups in genleral. In view of a result of G. D. Mostow ([3], Theorem on P. 12), in simply conniected solvable analytic groups, every closed uniform subgroup is a full subgroup. In section one, we give a condition when a full subgroup is a uniformll subgroup. We have the following theorem.