Martensitic transformation behavior of a series of Ti-(50-x)Ni-xCo at% alloys (x = 4, 8, 12, 16, 20) has been examined by electrical resistivity, magnetic susceptibility and specific heat measurements, in order to know the phase stability of the B2-type structure. The 4Co and 8Co alloys exhibit a typical first order B2-R-B19' transformation. The 12Co alloy probably transforms to the R-phase, but its microstructure is composed of small domains with about 10 nm in diameter, being quite different from the microstructure of a typical R-phase formed by nucleation and growth. The 16Co and the 20Co alloys do not show any martensitic transformation but anomalies of the electrical resistivity and magnetic susceptibility being similar to those of the 12Co alloy appear in these alloys. The diffuse scattering of 1/3<110> is also observed in the 16Co alloy. The Debye temperature decreases and electronic specific heat coefficient increases with increasing Co content.