in which each term is normal in its successor and each factor satisfies either the maximum or the minimum condition for subgroups. A group G has the subnormal intersection property if the intersection of each collection of subnormal subgroups of G is itself a subnormal subgroup of G, that is, if G contains a subnormal closure of every subgroup of G. For this to happen it is sufficient, but not necessary, that the defects of the subnormal subgroups are bounded. In [6] Robinson shows that a finitely generated soluble group has the subnormal intersection property if and only if it is finite-by-nilpotent. Hence, in particular, soluble groups satisfying the maximum condition for subgroups and having the subnormal intersection property must be finite-by-nilpotent. On the other hand a soluble group satisfying the minimum condition for subgroups is an extension of a periodic radicable abelian group by a finite group, by a well-known result of Cernikov [2], and as such it has the subnormal intersection property (see, for instance, Lemma 2.2 of [7]). In this paper we show that a soluble minimax group with the subnormal intersection property is an extension of a radicable abelian group satisfying the minimum condition by a (torsion-free nilpotent)-by-finite group (Theorem A). However a soluble minimax group with this structure need not have the subnormal intersection property, as the infinite dihedral group shows. Thus Theorem A does not give a complete picture of the structure of soluble minimax groups having the subnormal intersection property. The structure of these groups is probably rather complex. However there is a subclass of the class of groups under consideration which is easy to characterise. A soluble minimax group whose every subgroup has the subnormal intersection property is an extension of a group satisfying the minimum condition by a nilpotent group, and conversely every subgroup of a group in the latter class has the subnormal intersection property (Theorem B). The material in this paper forms part of a Ph.D. thesis for the University of London. I wish to thank my supervisor Dr. D. J. S. Robinson for his valuable