(Ni, Cu)-rich Ti–Ni–Cu amorphous films with a Cu content of 6.2–33.5 at. % formed by sputtering were annealed at 773, 873 and 973 K for 1 h and their microstructures investigated. Two types of precipitate were observed in the annealed films: a Ti(NiCu)2 phase for the Ti48.5Ni40Cu11.5, Ti48.6Ni35.9Cu15.5, Ti48.3Ni28.4Cu23.3 and Ti48.3Ni23.9Cu27.8 films, plus a TiCu phase for the Ti48.5Ni18Cu33.5 films. These precipitates were found to have coherency with the B2 matrix in the films annealed at 773 K and were densely distributed within the grains. However, in the films annealed at 873 K, their size increased 10-fold and their density decreased. Annealing at 973 K promoted grain-boundary precipitation and, accordingly, the density of the precipitates in the grain interiors decreased. On the other hand, the annealed Ti48.9Ni44.9Cu6.2 films showed no precipitates in their grain interiors, but the number of grain-boundary precipitates increased with increasing annealing temperature. It was also found that grain size decreased with increasing Cu content and was significantly decreased for the Ti48.5Ni18Cu33.5 films.