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This paper studies the behavior of SmAlO3 and NdAlO3 when they are subject to high pressures. This work is undertaken using angle-dispersive synchrotron x-ray powder diffraction and Raman spectroscopy at pressures up to 24.2 and 39.0 GPa, respectively. It is found that SmAlO3 undergoes an orthorhombic (Pnma) to rhombohedral (R-3c) structure transition at around 10 GPa; this transition is induced by the rotation of the AlO6 octahedra toward that of the ideal perovskite structure when the material is subject to high pressures. The tilting of the AlO6 octahedra also decreases at high pressures in NdAlO3. It is found that NdAlO3 maintains its original rhombohedral structure for pressures of up to 39.0 GPa. The structural changes observed in these compounds help establish the electrical and magnetic properties of RAlO3 (R = Sm or Nd) at high pressures.