Material properties of of rapidly solidified(RS),Ti5øNi5ø-xCux(X=O-2Oat%) alloys,i.e., thermoelasatic transformation temperature,transformation strain vs. temperature hysteresis, strength.ductility,themal fatigue resistance and corrosion resistance etc. were investigated. Specimens of thin ribbon were prepared by using melt-spinning machine with single Cu rolls at the cooling rate of about 40 m/sec. In the range of Cu content over lOat%,rapidly solidified (RS)ribbons were producible as a very thin plate and showed high ductility(i.e.180° bending). From the measurements of transformation strain vs. temperature hysteresis under small stress a bout 60MPa,transformation strain shows the maximum at Cu=5at%,and its transformtion temperature range nΔ(=Af-Mf) decreased with increasing Cu content to minimum value of 6.5K at Cu=17 at%. Thermal fatigue resistance was improved very much about ten times,futhermore,corrosion resistance was also improved over 100 times as much as conventionally processed(i.e. melting→ mechanically worked) material. It can be concluded that the functional superioity of RS meltspun Ti5øNi5ø-xCux ribbon exists in the range of Cu content over 10 at%. The reason of abovementioned remarkable improvements of material properties of RS TiNiCu alloys is discussed by relating with the observed unique fine columnar microstructures having strong crystal anisotropy and homogeneouss smooth surface.