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Stress–relaxation experiments were applied to cold-rolled Cu–10wt.%Zn, Cu–20wt.%Zn and Cu–30wt.%Zn alloys samples with different stacking fault energy (SFE). Relevant mechanical properties were tested by conducting tensile experiments. With a decrease of SFE, strength increased greatly without sacrificing ductility. Meanwhile, we found that a decrease in SFE leads to both a decrease in the variation of physical activation volume and the value of strain rate sensitivity but increases in exhaustion rate of mobile dislocations in copper alloys. This indicates that the deformation process is dominated by dislocation activities. The result provides an explanation for the mechanical behavior of some nanostructured materials which have high strength and not disappointingly low ductility.