In the field of mechanical engineering, the need for a simple but effective way of evaluating the fatigue strength and lifetime of structural materials is an important problem with which the design engineers have faced. Accordingly, a cunsiderable amount of investigations have been made in this field. However, the basic nature of fatigue damage and the conditions which lead to the initiation and propagation of fatigue cracks are not sufficiently understood. Nor any satisfactory method of assessing the exact state of fatigue damage has yet been found. X-ray diffraction technique is not a new as the method of experimental study, but has often been adopted for direct and non-destructive observations of change in the local structures of crystalline materials at fundamental research. X-ray technique is one of the most powerful means to investigate the changes of microscopic- structure due to external forces, considering the fatigue phenomena occur on the surface of materials. Accordingly, one of the authors have studied the relations of half-value breadth of X-ray diffraction lines, residual stresses and hardness and number of cycles of fatigue stresses in detail for various sorts of engineering metallic materials. In the results of a number of experiments, it has been found that the variation in half-value breadth showed very regular relation with number of stress cycles, the authors have reported that the lifetime of materials in fatigue could be predicted. Consequently, it needs to investigate whether or not this predicting method is fitted for alloy containg α and β phase, moreover, it is interesting to make clear the fatigue mechanism of such materials which are present two phases having the different yield stress and type of crystal structure.