Dynamic grain evolution of a magnesium alloy AZ31 was studied in compression at 673 K (0.73T_m) by optical and SEM/OIM microscopy. The flow curve shows rapid hardening accompanied by a stress peak at a relatively low strain (ε_p=0.12), followed by strain softening and then a steady state flow stress at high strains. Fine grains evolved at corrugated grain boundaries at around ε_p and developed rapidly during strain softening, finally leading to a full structure of equiaxed fine grains. Such characteristics of new grain evolution and flow behavior are apparently similar to those in conventional, i.e. discontinuous, dynamic recrystallization (DRX). On the other hand, kink bands were observed frequently near corrugated grain boundaries and also in grain interiors, even around ε_p. The misorientation of the boundaries of the kink bands increases rapidly during strain softening and approaches a saturation value of around 43^° at high strains. The average size of the regions fragmented by kink bands is almost the same as that of the new grains. It is concluded, therefore, that new grain evolution in this alloy is controlled by a deformation-induced continuous reaction, i.e. continuous DRX.