Reactive MBE growth was used to synthesize ferromagnetic Cr-doped GaN and AlN thin films with Curie temperatures above 900K. 2% Cr-doped GaN and 7% Cr-doped AlN were found to have a saturation magnetization moment of 0.42 and 0.6 μ B /Cr atom, indicating that ∼14% and ∼20% of the Cr, respectively, are magnetically active. Structural characterization using X-ray diffraction (XRD) and transmission electron microscopy (TEM) did not find evidence of a ferromagnetic secondary phase. Electrical characterization indicate that the resistivity of the Cr-doped GaN films depends exponentially on temperature as R=Roexp[(To/T)1/2], characteristic of variable range hopping. In contrast, Cr-doped AlN films are highly resistive. Local spin density functional calculations predict that Cr forms a deep level defect in both systems and the t2 level falls approximately at midgap. Our theoretical and experimental results indicate that ferromagnetism in Cr-doped GaN and AlN arises as a result of the double exchange mechanism within the partially filled Cr t2 band.