The martensitic transformations in a dual-phase α/β Cu-Zn shape-memory alloy, containing 15 pct by volume of α particles, were studied during subcooling and deformation. The crystal structure and characteristics of the martensitic transformation of a dual-phase Cu-Zn alloy were found to be similar to those of a single-phase alloy. Both the thermal martensite formed by subcooling and the stress-induced martensite (SIM) formed by loading possessed an M9R long-period stacking-order (LPSO) structure, with internal stacking faults on the (001) basal plane. Upon subcooling, the α particles were deformed in order to accommodate the shape strain accompanying the martensitic transformation. Although most of them are deformed by slip, deformation twins have, nevertheless, been found in a few α particles. Upon loading, the SIM with an M9R structure nucleates and grows at a given temperature; subsequently, another martensite phase (αs) possessing an fct structure is formed, with a shear developing on the basal plane of the initial M9R SIM during further loading. However, during unloading, both the αs and SIM are transformed and follow the reverse sequence back to the parent phase. However, some residual SIM and αs were found at zero load, due to a constraint effect of the deformed α particles and grain boundaries. The α martensite may be formed by two intersecting plates of SIM or by advanced deformation on a single plate of SIM. In addition to the residual SIM and αs martensite, an SIM/αs lamellar martensite was found in the deformed specimen.