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AlN, GaN, and InN were irradiated at room temperature with monatomic swift heavy ions and high-energy fullerenes. Ion track formation was studied using transmission electron microscopy in both plane view and cross-sectional modes. A full experimental description of ion track formation in these compounds is presented. AlN shows a remarkable resistance towards track formation; InN is the most sensitive and shows partial decomposition, likely into N and metallic clusters; the overlapping of the amorphous tracks in GaN does not give an amorphous layer because of a track-induced recrystallization. We discuss the application of the inelastic thermal spike model, which allows good and simple predictions of track radii in oxides, to the studied III-nitrides, and in general to semiconductors. [ABSTRACT FROM AUTHOR]