The core structure of threading dislocations in Mg-doped Al0.03Ga0.97N thin films was examined using transmission electron microscopy. It was demonstrated that edge and mixed dislocations in Mg-doped Al0.03Ga0.97N films can have hollow cores with diameters in the range of 1-5 nm. A model was presented in which hollow core formation is initiated by the segregation and subsequent precipitation of Mg at these dislocation cores.