Alloys with a thermoelastic martensitic transformation generally exhibit high mechanical damping in the martensitic phase. Further in this type of alloy a strong internal friction maximum versus temperature is observed during transformation. This maximum is heating rate dependent. This work is concerned with the decrement measurement in a Cu-Zn-Al alloy at zero heating rate. In this case, and at temperatures below Ms, it has been shown that internal friction decreases with the number of measuring oscillations, and recovers after a few minutes'rest. The residual internal friction after a large oscillation number does not exhibit any peak at transformation temperature and is stress dependent in the martensitic region. This behavior is qualitatively explained in terms of a very simple model. (Received November 16, 1979)