In this paper we determine the structure of the soluble groups in which every proper subgroup is an intersection of maximal subgroups. Our main result is: A group G is soluble and every subgroup H of G is the intersection of the maximal subgroups of G containing H if and only if G has a normal Hall subgroup N such that (i) N is elementary abelian, (ii) G/N is elementary abelian, and (iii) every element of G induces on N a "power automorphism"