Transformation behaviors and shape memory characteristics of Ti-45Ni-5Cu alloy ribbons fabricated by melt spinning were investigated by means of optical microscopy, differential scanning calorimetries(DSC), X-ray diffraction and thermal cycling tests under constant load. They depended largely on temperatures of liquid metal. The B2-B19-B19' two-step transformation occurred in the ribbons fabricated with the liquid whose temperature,was higher than 1723 K, while the B2-B19' one-step transformation occurred in the ribbons with the liquid at 1673 K. The stabilization of the B19 martensite in Ti-45Ni-5Cu alloy ribbons was ascribed to the high density of dislocations which made strong resistance to large lattice deformation associated with a formation of the B19' martensite.