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The superplasticity of an extruded fine-grained Mg–9Gd–4Y–0.4Zr alloy was investigated by measuring the strain rate sensitivity using shear punch testing (SPT). Shear punch tests were conducted at shear strain rates in the range of 3 × 10−3–2 × 10−1 s−1 and at temperatures in the range of 573–773 K. The results indicate the strain rate sensitivity, m, increases from about 0.11 at 573 K to about 0.40 at 723 K and then decreases to 0.32 with a further increase in test temperature. A strain rate sensitivity of 0.40 and an activation energy of 140 kJ/mol are indicative of a superplastic deformation behavior dominated by grain boundary sliding accommodated by lattice diffusion at temperatures above 673 K.