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We report on the ferromagnetic resonance studies on ZnMnO films grown by the pulsed-laser deposition technique. ZnMnO films were annealed in different atmospheres. The films grown and annealed in oxygen demonstrate ferromagnetic behavior at room temperature and below. However, annealing in either nitrogen or argon deteriorates the ferromagnetic response of the films. Further annealing the films in oxygen recovers the ferromagnetic response. Our results suggest that oxygen plays a major role for controlling the ferromagnetic properties in ZnMnO films.