The damping property tan 0 of Cu-Al-Mn-based alloys, where tan 0 is nearly equal to internal friction Q À1 , was investigated using a Dynamic Mechanical Spectrometer (DMS). It was found that the dependences of frequency and strain amplitude on tan 0 are significantly different between the parent + martensite two-phase and the martensite single-phase states, i.e., tan 0 is mainly influenced by frequency in the two-phase state and by strain amplitude in the martensite state. It was also found that the relative grain size d=D is a function of the damping capacity, where d and D are the grain diameter and the diameter of the wire, respectively, and that tan 0 increases with increasing d=D. The maximum values of tan 0 ¼ 0:54 and tan 0 ¼ 0:07 were obtained in the two-phase state and in the martensite state, respectively, in the specimen of d=D % 1.