From an analysis of the room temperature nuclear resonance of ²⁷Al principal values are obtained for the electric field gradient eq V_zz/h and the anisotropy constant eta at an aluminium site for GdAlO₃ (0.589+or-0.01 MHz and 0.878), TbAlO₃(0.890+or-0.01 MHz and 0.01 MHz and 0.613) and DyAlO₃ (1.30+or-0.03 MHz and 0.655). The directions of the principal axes of the electric field gradient relative to the crystal axes are obtained. At low temperatures the nuclear resonance of ²⁷Al is measured in GdAlO₃ in the paramagnetic region (T>3.87 K) and the antiferromagnetic region (1.4 K<T<3.87K). The results obtained are shown to agree with a simple model based on the currently held view of the ordered magnetic structure of this salt. There remains a large discrepancy between the magnitude of the observed internal magnetic field at an ²⁷Al site and that calculated assuming classical magnetic dipole coupling. The possibility of a large anisotropic transferred hyperfine interaction is discussed.