Small spherical samples (diameter approximately 2 mm) of NdBa 2 Cu 3 O 7−␦ (Nd123) were fully melted in Ar gas flow in an aero-acoustic levitation device and subsequently rapidly cooled by splat quenching. For samples quenched above the liquidus, the microstructual and x-ray-diffraction (XRD) observations suggested the existence of the amorphous phase with small quantities of the BaCuO 2 and BaCu 2 O x . The high-temperature XRD results indicated that the decomposition of the amorphous phase, probably assisted by atmospheric CO 2 and H 2 O, led to formation of the BaCO 3 phase at 400°C and, subsequently, the Nd123 phase was formed by the solid diffusion above 800°C. Another set of Nd123 samples was fully melted in O 2 gas flow, undercooled while levitated, and then splat quenched at a temperature below the peritectic temperature (T P ). These samples possessed a microcrystalline microstructure of the Nd123 phase that was confirmed by XRD. This indicated that the Nd123 phase was solidified directly from the undercooled melt quenched below T P .