Internal friction and elastic modulus of Mn-Cu alloys containing 60 and 70 wt % Mn and of Mn-Cu-Al alloys containing about 40 wt % Cu, 1.92-3.59 wt % Al were measured with acoustic frequency in the temperature range of -150 to 150°C. The martensitic transformation peak and the twin boundary relaxation peak which did not appear before ageing were observed above room temperature after a definite ageing time in the temperature range under the spinodal curve within the miscibility gap. It is shown that the transformation peak proper is originated from the stress-induced movement of the interface boundaries between the parent phase and the transformation product, and the internal friction background at the low-temperature side of the transformation peak which exhibits a very strong amplitude effect and shows a strong non-linear behaviour, is originated from the hysteretic movement of the martensite-martensite interfaces. It has also been found that the addition of aluminium enhances the strength but reduces the internal friction of the specimen. A choice of suitable ageing time and temperature can give an optimum compromise of high strength and high internal friction