Cu-Al-Ni alloys, similarly as other Cu-base shape memory alloys, transform into more martensitic structures alpha(1)' (6R), beta(1)' (18R) and gamma(1)' (2H), depending on the temperature, stress, load axis orientation, sense of loading and composition. The transformation stress-temperature conditions at which individual transitions take place are beneficially represented in so called non-equilibrium stress-temperature phase diagrams. On the basis of the sigma-T diagrams, complex history dependent thermomechanical behaviors of SMA single crystals undergoing sequentially multiple solid state transitions can be easily understood and predicted. Since chemical composition of the alloy crystals affects mainly the equilibrium transformation temperatures, T(0), and only slightly the slopes of the transformation lines in the sigma-T diagrams, the diagrams mainly shift in the temperature range (over similar to200K) with the compositional variations. The shape of the diagrams, however, may change significantly when the T(0) shifts for individual transitions are different. Knowledge of the compositional dependence of sigma-T diagrams would be beneficial for the development of shape memory alloys with specific required thermomechanical properties. The aim of the present work is experimental investigation of the martensitic transformations and construction of the sigma-T diagram for Cu-Al-Ni alloy with lower At content (T(0)>363K) and comparison with our previous results obtained on alloys with higher At content (T(0)<263K).