By means of X-Ray diffraction, hardness test and microscopic examination, the change in structure of an aluminium-copper alloy (3.4% copper) and Duralumin, that have been quenched, in the ageing and tempering at room and higher temperatures ranging from 150° to 350° is studied. In the ageing temperatures between 150° and 200° complete agreement is obtained between the maximum width of diffraction and maximum hardness but there is no broadening of diffraction in spite of marked variation in hardness immediately after quenching, ageing at room temperature, and heating at 150° for one hour. This may be explained as follows: The lattice of the alloy immediately after quenching is in more contracted state in general compared with that of the alloy aged between 150° and 200° due to separation. Any further contraction is accompanied by unproportionately large increase in stress. In other words, it is not difficult to assume that in spite of long time necessary for ageing the actual shifting of the foreign atom is very small, resulting in no practical change in the width of diffraction. On the other hand, in ageing between 150° and 200° there is some separation of the foreign atom, which results less contraction of the lattice as a whole. Under tlhis condition comparatively a large distortion will cause a small stress. Therefore, in order to produce an internal stress of lattice which indicates such degree of hardness as shown in the experiment, rather a large increase in distortion of the lattice must teen accompanied causing an increase in width of diffraction.