The effects of ageing at 473–573K on the hardness, microstructure and thermoelastic martensitic transformation in Cu–Al–Mn-based shape memory alloys were investigated. It was found that hardness was dramatically increased by ageing due to the formation of fine bainitic plates and that the volume fraction of the bainite phase with ageing time can be described by the Austin–Rickett equation. The martensitic transformation temperatures decreased with the formation of bainite plates, mainly due to the composition change of the β-matrix. Moreover, the growth of thermally induced martensite plates was disturbed by the existence of bainite plates. Consequently, the transformation intervals (M s –M f and A f –A s ) and transformation hystereses (A f –M s and A s –M f ) increased with the progress of bainitic transformation.