The spectra of spontaneous and stimulated ultraviolet luminescence of ZnO nanorods annealed in air are studied at the temperature 4.2 K. The emission peaks corresponding to bound and free excitons and excitons interacting with excitons and exciton-impurity complexes are detected. It is found that high-temperature annealing induces an increase in the crystallite dimensions and a decrease in the number of point defects in the crystal structure of the nanorods. It is established that stimulated ultraviolet luminescence is initiated due to inelastic interaction of excitons in the case of increasing optical pumping intensity.