Equal channel angular pressing (ECAP) technique had been adapted to the Mg alloy (AZ31) for achieving effective grain refinement through severe deformation. The average grain size of $2.5{mu}m$ could be obtained after 4 passes. The stability of the ECAPed structure at elevated temperatures was examined by annealing the ECAPed materials over a wide range of temperature between 473 and 748 K. The average activation energy, Q, for static grain growth of 1, 2 and 3 passes was 33.7 kJ/mole (=0.25QL, activation for lattice diffusion). The abnormally low Q value in the lower temperature range may indicate that grain growth occurs in the unrecrystallized microstructure where non-equilibrium grain boundaries containing a large number of extrinsic dislocations exist. The yield stresses of the ECAPed alloys decreased whereas the elongations increased after the ECAP process. These results should be related to the modification of texture for easier slip on basal plane.