The character and mechanism of two-way shape memory (TWSM) “training” has been investigated in a Cu-Zn-Al alloy by means of detailed thermomechanical evaluation and TEM observations. The progressive effects of training on the TWSM behaviour, as well as an accompanying substructural evolution, have been established. The results indicate a relationship between the substructural effects of cyclic thermoelastic martensitic transformation and the ability to exhibit TWSM. Microscopic studies reveal that as the number of cycles of thermoelastic transformation under stress increases, specific physical features develop in the parent phase submicrostructure. These take the form of dislocation structures which evolve into “vestigial” martensite markinqs. These in turn assist in the nucleation and growth of a preferred martensite plate arrangement on cooling which is similar to that induced under stress during the training cycles.