The mechanism of ultraviolet stimulated emission was investigated in ZnO/ZnMgO multiquantum wells. Stimulated emission induced by exciton-exciton scattering occurred throughout a range of temperatures from 5 K to room temperature. At temperatures higher than 160 K, stimulated emission due to electron-hole plasma recombination was also observed with a higher excitation threshold than that of exciton-exciton scattering. The exciton binding energies of multiquantum wells were larger than that of bulk ZnO and increased with a decrease in the well widths. This enhancement of exciton binding energy is due to the quantum-confinement effect and is favorable for the stability of exciton states.