Methods of transmission and scanning electron microscopy and chemical microanalysis, electron diffraction, and X-ray diffraction were used to study the structure and the chemical and phase composition of ribbons of the four-component quasi-binary alloy Ni45Ti32Hf18Cu5. The influence of the synthesis regimes and subsequent heat treatment of the alloy on the formation of the amorphized state and ultrafine-grained structure has been determined. The critical temperatures of the devitrification and of the B2 ↔ B19' thermoelastic martensitic transformation have been established based on the data of the temperature dependences of the electrical resistivity. The lattice parameters of the B2 and B19' phases and the (Ti,Hf)2Ni phase have been determined by X-ray diffraction. The mechanical properties of the alloy were determined in tensile tests, and the shape-memory effects in the ribbons of the alloy were measured using bending tests.