Phase-mix, phase transformations and crystallographic texture of amorphous/nanostructure melt-spun ribbons of Ti2NiCu were studied using X-ray diffraction and nano-indentation. Their peak two-way shape-memory effect occurs when most of the austenite (cubic, B2) phase has converted to martensite (orthorhombic, B19), but before grain growth takes place. The melt-spinning process imparts strong B2 {100} texture that is retained as B19 (100) and (011) after phase transition during subsequent annealing. Because the phase transformation and texture strongly depend on the annealing process, it should be possible to tailor them for further improving their performance.