Shape memory alloys (SMA) such as Ti-Ni are widely used in the biomedical field due to their unique functions of shape memory effect (SME) and superelasticity (SE). However, a drawback of Ti-Ni SMAs in the biomedical applications is the toxicity of the constitute element Ni, in other words, Ni hypersensitivity. Thus we have conducted to develop new Ni free SMAs composed of non-toxic elements as a new class of biomedical functional materials. In the present study, the mechanical and shape memory properties of some Ti-base shape memory alloys we have found are described. The alloy systems selected were Ti-Nb-Al and Ti-Nb-Ga. Both the alloys were made by Ar arc melting method followed by a homogenization treatment at 1273K for 7.2ks, cold rolling and then a solution treatment at 1273K for 1.8ks. Tensile tests were done to evaluate SME and SE. It was found that both TiNbAl and TiNbGa alloys exhibit SE at room temperature, and that the SE behavior changes depending on the deformation strain. 2.4% superelastic strain obtained for the TiNbAl alloy after the cyclic deformation of 3.2%. Besides the SE behavior becomes stable after two cyclic deformation under the constant maximum. strain. It is summarized that these Ti-base SMAs exhibit large potential for practical biomedical use.