Transmission electron microscopy is used to investigate the structure of inversion domain boundaries in α-GaN (0001) films grown by metal-organic chemical vapour deposition on sapphire substrates. Convergent-beam electron diffraction is used to establish the existence of inversion domains with (1010) boundaries. Displacement fringes observed in two-beam images recorded from inclined inversion domain boundaries are compared with dynamical simulations. It is shown that the results are consistent with an atomic model in which fourfold bonding is preserved with all bonds being of the Ga-N type. The significance of the results for understanding the electronic properties of GaN is briefly discussed. © 1998 Taylor and Francis Group, LLC.