Elastic moduli (Young's modulus, shear modulus and bulk modulus) of three ultrafine-grained Mg-based alloys AZ31, AE42 and LAE442 were studied by resonant ultrasound spectroscopy. Evolution of these moduli and the corresponding high-frequency internal friction were measured in a temperature cycle between the room temperature and 310 A degrees C, i.e., with heating above the recrystallization threshold temperature. The results reveal that the Li content in the LAE442 alloy has a strong impact on its elastic performance, resulting in a high E/rho ratio, which is consistent with predictions of ab initio calculations. Simultaneously, the relaxation due to grain boundary sliding has significantly lower activation energy in LAE442 alloy.