The hypoperitectic Ti47Al53 alloy was cyclically superheated in a containerless electromagnetic levitation apparatus in order to reach the state of supercooling. The maximum undercooling of the alloy melt was up to 250K. Critical undercooling ranges for the formation of various competing phases were determined by transmission electron microscopy. The primary phase beta in 0 K < Delta T < 36 K, the primary phase a in 36 K < AT < 120 K, and the primary phase gamma in 120K < Delta T < 250K were determined by microstructure analysis. The transient nucleation theory was adopted to explain the phase evolution relationship in the undercooled melt on the consideration of the competing phase with the shortest incubation time having separated from the undercooled melt. Due to different structures of primary and secondary phases, clear fault ribbons from beta to alpha (or alpha to gamma) were detected on the boundary layer between primary and secondary phases. The reason for the formation of fault layers on the boundary layer was given with a view of the crystalline structure evolution.