Ti-Ni and Ti-Ni-Cu thin films were prepared by r.f. magnetron sputtering. The compositions were determined by electron probe X-ray microanalysis, the Cu content ranging from 0 to 13.7 at.%. Transformation and deformation characteristics and lattice constants of these thin films were investigated by differential scanning calorimetry and X-ray diffractometry. The martensite transformation temperatures of the Ti-Ni-Cu films were around 323 K. The hysteresis associated with the transformation shows a strong dependence on Cu content, i.e. it decreases from 27 K to 10 K with Cu content increasing from 0 to 9.5 at.%. In Ti-Ni-Cu with Cu content less than 9.5 at.%, a single-stage transformation occurs between the B2 and monoclinic phases. At 9.5 at.% Cu, there is a two-stage transformation B2 <-> orthorhombic <-> monoclinic; the lattice parameters of these phases were determined by X-ray diffractometry. In Ti-Ni-Cu with Cu content higher than 9.5 at.%, the second-stage transformation orthorhombic <-> monoclinic is not observed. The transformation characteristics of the thin films were compared with those of bulk specimens.