The mechanical fatigue life and tensile property of a Ti-41at.%Ni-8.5at.%Cu alloy, which was solution-treated after some thermo-mechanical treatments, were investigated at 370±1 K as a function of deformation speed. The tensile properties were also investigated at 295±1 K as a function of deformation speed. The B2→B19 martensitic transformation start temperature, Ms, of the alloy was determined to be 338 K by a differential scanning calorimetry, while that of the as-rolled alloy could not be determined. Two types of fatigue tests were carried out by using plate-shaped specimens of 3.5 mm width and 1.5 mm thickness with sinusoidal waveform stresses of 20 Hz and 0.5 Hz frequencies being applied respectively. The fatigue life obtained from the 20 Hz tests was superior to that from the 0.5 Hz tests, the former being about 2 times longer than the latter at the same stress level. Tensile tests were performed at three tensilem speeds of 8.3 × 106, 8.3 × 10−5 and 8.3 × 10−3 m/s. In all the stress - strain curves obtained, an apparent yielding was observed after the liner elastic deformation. The apparent yielding is due to the occurrence of martensitic transformation. The critical stress for inducing martensite and tensile fracture stress increased with increasing tensile speed. Therefore, it is clear that fatigue and tensile properties of Ti-Ni-Cu shape memory alloys are strongly affected by not only test temperature but also deformation speed.