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 (b phase! towards a close-packed structure (M phase!. Negative magnetoresistance that shows an almost linear dependence on the square of magnetization with different slopes in the M and b phases was observed. This magnetoresistive effect has been associated with the existence of Mn-rich clusters with the Cu2AlMn structure. The effect of an applied magnetic field on the martensitic transition has also been studied. The entropy change between the b 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 Cu2MnAl-rich domains that do not transform martensitically.