Multinuclear 71Ga, 69Ga, 27Al and 17O NMR parameters of various polymorphs of LaGaO3 and LaAlO3 perovskites were obtained from the combination of solid-state MAS NMR with solid-state DFT calculations. Some of the materials studied are potential candidate electrolyte materials with applications in intermediate temperature solid oxide fuel cells (ITSOFCs). Small variations in the local distortions of the subject phases are experimentally observed by 71Ga (and 69Ga) and 27Al NMR in the LaGaO3 and LaAlO3 phases, respectively, with heating to 1400 K. The orthorhombic-to-rhombohedral phase transformation occurring in LaGaO3 at approximately 416 K is clearly observed in the 71Ga/69Ga NMR spectra and is associated with a significant increase in the quadrupolar coupling constant (QCC). Thereafter a gradual decrease in QCC is observed, consistent with increased motion of the GaO6 octahedral units and a reduction in the degree of octahedral tilting. The experimental and theoretical 71Ga, 69Ga, 27Al and 17O NMR parameters (including isotropic and anisotropic chemical shift parameters, quadrupolar coupling constants, and associated asymmetries) of the low and high temperature polymorphs are compared. In general, the calculated values display good agreement with experimental data, although some significant deviations are identified and discussed.