beta'-Sialons (Si6-zAlzOzN8-z, where 0 <= z <= similar to 4.2) are studied using a combination of Si-29 and Al-27 solid-state NMR, using magnetic fields of up to 20 T, powder X-ray diffraction, and density functional theory (DFT) calculations of both the structure and NMR parameters. Four different structural models have been proposed in the literature for the replacement of silicon and nitrogen by aluminum and oxygen within a beta-Si3N4 structured lattice. Experimental data are presented for the variation with composition (z) of the unit cell parameters from diffraction and the local coordination units present suggested by NMR data. The experimental data are compared to the changes with composition in the DFT calculations of the structure and the NMR parameters according to the four models, allowing the models to be distinguished. It is shown that only one of these, the domain model, is fully consistent with all of the experimental data and is, therefore, a good structural model for beta'-sialons. More speculatively, it is suggested that for the domain model, Al-27 NMR data might provide a constraint on the thickness of its aluminum-rich layers.