Cu-Al-Mn shape memory alloys in the range of 10-15 wt.% of aluminum and 0-10 wt.% of manganese, exhibiting β-phase at high temperatures and manifesting shape memory effect upon quenching to lower temperatures, were prepared through ingot metallurgy. The damping behavior of the alloys was studied using a dynamic mechanical analyzer. The damping capacity of the alloys increases with an increase in the aluminum content when the Cu/Mn ratio or amount of manganese is maintained constant. The damping capacity of the alloys decreases with an increase in the manganese content when the Cu/Al ratio or the amount of aluminum is maintained constant. The alloys exhibit an internal friction peak in the transition zone and that all of them exhibit higher damping capacity in the martensitic condition compared with that in the austenitic condition. While ageing of the alloys at 300 °C increases the transformation temperatures of the alloys, there is a reduction in the damping capacity of the alloys due to the formation of precipitates. The alloys aged at 500 °C do not exhibit the austenite to martensite transformation due to the formation of precipitates rich in aluminum and therefore exhibit very poor damping capacity. © 2007 Elsevier B.V. All rights reserved.