Abstract Thermally and stress induced martensitic transformations between β and a mixture of martensitic structures, β′ and γ′, were studied in Cu–14.1Al–4.2Ni (wt%) single crystals. In this way information on the relative stability between β′ and γ′ martensites, compared to the β phase, was obtained. The measurement of electrical resistance as a function of temperature was used to follow the evolution of thermally induced transitions. The stress induced transformations were analyzed in the small temperature range at which the pseudoelastic behavior between β and a mixture of both martensites plays the main role. A clear inhibition of the γ′ martensite is detected as the number of cycles increases, no matter which thermodynamic coordinate is varied to induce the phase transition, i.e., temperature or stress. An evaluation of the magnitude of the relative stabilization of the β′ martensite compared with γ′ was obtained by a suitably designed experiment.