Shape memory alloys take place in a class of smart materials by exhibiting a peculiar property called shape memory effect. This property is characterized by the recoverability of two certain shapes of material at different conditions. Shape memory effect is based on dual crystallographic phase transformations, thermal and stress induced martensitic transformations in atomic scale. Thermal induced martensitic transformation occurs on cooling along with lattice twinning with cooperative movements of atoms in atomic scale, and ordered parent phase structures turn into twinned martensite structures. Product phase occurs as martensite variants with this transformation by means of the lattice invariant shears in -type directions on the {110}-type planes of austenite matrix, and twinned martensite structures turn into the detwinned martensite structures by means of stress induced martensitic transformation by stressing material in the martensitic condition. Martensitic transformations have diffusionless character and movements of atoms are confined to inter atomic distances. Shape memory effect is initiated by successive cooling and deformation treatments, and activated thermally on heating and cooling. These alloys are plastically deformed in martensitic condition, with which strain energy is stored in the materials keeping the deformed shape, and released on heating by covering original shape on heating. These materials cycle between original and deformed shapes on heating and cooling, respectively in reversible shape memory effect in bulk level; whereas the crystal structure cycles between the twinned and ordered parent phase structures. Microstructural mechanisms responsible for the shape memory effect are the twinning and detwinning reactions. It is well known that twinning and detwinning play a considerable role in shape memory behaviour of materials. Copper based alloys exhibit this property in metastable β-phase region, which has bcc based structures. Lattice invariant shears are not uniform in these alloys, and the ordered parent phase structures martensitically undergo the non-conventional complex layered structures on cooling. The long-period layered structures can be described by different unit cells as 3R, 9R or 18R, depending on the stacking sequences on the close-packed planes of the ordered lattice. The unit cell and periodicity is completed through 18 layers in direction z, in case of 18R martensite, and unit cells are not periodic in short range in direction z. In the present contribution, x-ray diffraction and transmission electron microscopy studies were carried out on two copper based CuZnAl and CuAlMn alloys. X-ray diffraction profiles and electron diffraction patterns reveal that both alloys exhibit super lattice reflections inherited from parent phase due to the displacive character of martensitic transformation. X-ray diffractograms taken in a long time interval show that diffraction angles and intensities of diffraction peaks change with the aging time at room temperature. This result refers to a new transformation in diffusive manner.