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We report the magnetic properties of Cr-doped AlN thin films grown by reactive magnetron sputtering under various nitrogen pressures. Ferromagnetism is observed up to the highest temperature measured, 400 K, and shows strong dependence on the Cr concentration and, especially, the nitrogen growth pressure. By varying the nitrogen pressure during film growth, the magnetic properties of the films can be changed while keeping a constant Cr concentration. The ferromagnetism is enhanced in the films that were grown at low nitrogen pressures and thus nitrogen deficient, suggesting an important role of defects in the ferromagnetism of this material.