The icosahedral quasicrystalline, amorphous plus crystalline and glassy phases were formed in Ti40βZr20βHf20β(3dβLTM)20β alloys (3d-LTM = 3d late transition metals Fe, Co and Ni). The icosahedral phase formed in the melt-spun Ti40βZr20βHf20βFe20β alloy is metastable and the average size ofthe quasicrystalline icosahedral particles precipitated in the amorphous matrix is 5 nm. The metastable icosahedral phase transformed to a big-cubic fcc Hf2βFe phase with the grain size of about 20 nm after annealing for 1.8 ks at 841 K. The glassy phase was formed in the melt-spun Ti40βZr20βHf20βCo20β alloy and no metastable phase was found to form during the transformation from glassy phase to a stable crystalline phase. Icosaheadral phase formed in the melt-spun Ti40βZr20βHf20βNi20β alloy transformed to a big-cubic fcc (Zr,Ti)2β Ni solid solution phase by a solid state reaction