We have studied the effect of ageing within the miscibility gap on the electric, magnetic, and thermodynamic properties of a nonstoichiometric Heusler Cu-Al-Mn shape-memory alloy, which undergoes a martensitic transition from a bcc-based structure ( phase͒ towards a close-packed structure (M phase͒. Negative magnetoresistance that shows an almost linear dependence on the square of magnetization with different slopes in the M and  phases was observed. This magnetoresistive effect has been associated with the existence of Mn-rich clusters with the Cu 2 AlMn structure. The effect of an applied magnetic field on the martensitic transition has also been studied. The entropy change between the  and M phases shows negligible dependence on the magnetic field, but it decreases significantly with annealing time within the miscibility gap. Such a decrease is due to the increasing amount of Cu 2 MnAl-rich domains that do not transform martensitically.