One-stage pseudoelasticity associated with the consecutive β₁\ ightleftarrowsβ₁′\ ightleftarrowsα₁′ transformations in a Cu-14.4Al-3.6Ni (mass%) alloy has been examined in detail by tensile testing and metallographically observing single crystals with near ⟨001⟩ orientations. On the basis of the experimental results, the occurrence of the consecutive transformations was thermodynamically analyzed by taking into account the stress hysteresis of each transformation. As a result, the following points are clarified: The α₁′ martensite forms in crossed regions of two variants of the β₁′ martensite stress-induced from the β₁ parent phase as in the case of Cu–Zn–Al alloys. The consecutive transformations are observed to occur in a temperature range between two critical temperatures, where the critical stress for β₁→β₁′ transformation becomes equal to that for the β₁′→α₁′ transformation and where the critical stress for the α₁′→β₁′ transformation becomes equal to that for the α₁′→β₁′ transformation, respectively. Temperature dependence of the equilibrium stress for the β₁\ ightleftarrowsα₁′ transformations has been calculated on the basis of the Clausius-Clapeyron equation, by using observed temperature dependencies of the equilibrium stresses and calculated transformation elongations for the β₁\ ightleftarrowsβ₁′ and β₁′\ ightleftarrowsα₁′ transformations. It is thus concluded that the direct β₁→α₁′ transformation is difficult to experimentally observe in Cu–Al–Ni alloys, being different from the case of Cu–Zn–Al alloys.