In situ observations have been made of the first-order phase transition occurring at approximately 145-degrees-C in a large LaGaO3 single crystal, and the second-order phase transition occurring at approximately 435-degrees-C in a large LaAlO3 single crystal, using synchrotron white beam x-ray diffraction topography. Twin structures in both crystals at room temperature were revealed on reflection x-ray topographs. The images of twinned regions have positional shifts with respect to those of matrix regions. In the case of LaGaO3, the high-temperature rhombohedral phase reflections gradually replace the low-temperature orthorhombic reflections as the transition temperature is approached. The twinning configuration in the orthorhombic phase changes with temperature, and is eventually replaced by a different kind of twinning in the rhombohedral phase. In the case of LaAlO3, the magnitude of this image shift continuously decreased in magnitude as the temperature approaches the transition point, which along with the gradual distortion of the diffraction pattern, confirms the second-order nature of this transition. As the transition temperature is surpassed, twinning completely disappears in the crystal, as expected, since the twin planes in the rhombohedral phase become mirror planes in the cubic phase. As the crystal is cooled down through the transition, twins are seen to re-nucleate in the crystal, although the final twin density is reduced. The effects of both the transitions and the twinning on the use of these materials as substrates for high-T(c) superconductor Ba2YCu3O7-delta epilayers are briefly discussed.