High-pressure transitions of Ga2O3 and In2O3 were examined by using a laser-heated diamond-anvil cell combined with in situ x-ray diffractometry at pressures up to 108 GPa and 20 GPa, respectively. To predict the transition pressure to high-pressure phases, first principles static lattice energy calculations based on the density functional theory were also performed. Rh2O3(II) phases were confirmed as post corundum phases for both Ga2O3 and In2O3 at about 37 GPa and 7 GPa, respectively. The transition pressures determined by high-pressure experiments are almost consistent with those by theoretical computations. In regard to the present sesquioxides, a link of transition from corundum to perovskite was not confirmed. The Rh2O3(II) phases converted to corundum phases under decompression at room temperature. The bulk modulus of Rh2O3(II) phase in Ga2O3 and In2O3 were determined as 271 +/- 10 GPa and 169 +/- 4 GPa with their pressure derivatives fixed at 4, respectively.