The B2\ ightleftarrowsB19 and B19\ ightleftarrowsB19′ transformations in a ternary 50Ti-40Ni-10Cu (at.%) alloy were investigated by means of electrical resistivity measurements, differential scanning calorimetry and constant load thermal cycling tests, and they were compared with the B2\ ightleftarrowsR and B2\ ightleftarrowsB19′ transformations in a thermo-mechanically treated binary 49.8Ti–50.2Ni alloy. The B2\ ightleftarrowsB19 transformation in the ternary alloy under load took place within a narrow temperature range (2 to 5 K), whereas the B19\ ightleftarrowsB19′ transformation took place over a wide temperature range (>80 K). The transformation start temperature of B2→19 transformation increased with increasing applied stress, but that of B19→B19′ remained unchanged with stress when the stress was below 30 MPa. The stress dependence of the transformation start temperature, transformation elongation and hysteresis of the B2\ ightleftarrowsB19 transformations in the ternary alloy were 8.4 MPa/K in the reciprocal form (dσ⁄dT) where σ is the critical stress for inducing the transformation, 3.2% and 11 K, respectively. They were in-between those of the B2\ ightleftarrowsR and B2\ ightleftarrowsB19′ transformations in the binary alloy.