Over the last thirty-five years there has been a major effort to understand the structure of groups in which every subgroup is subnormal. This culminated in the important result of Möhres that such groups are soluble. Here the author studies torsion-free groups with every subgroup subnormal and he improves his previous result by showing that such groups are nilpotent. This is, of course, in contrast to the well-known non-nilpotent examples of Heineken and Mohamed, which are torsion groups. The proofs of the current result involve considerable ingenuity, as well as much previous work.