In the present work a monocrystalline Cu-13.5AI-4Ni (wt.%) alloy with shape memory effect (SME) submitted to thermal cycling inside the critical range was investigated in terms of number of cycles and resulting structural changes. Attention was paid to the structural changes associated with reversible beta(1)<->gamma'(1), martensite transformation. The monocrystalline Cu-Al-Ni alloy was produced in Russia, according to a specific technology. The structural characteristic of the alloys was studied through optical microscopy and X-ray diffraction methods using Cu-Kc, radiation. Differential scanning calorimetry permitted the determination of the temperature range as well as a thermal effect due to the beta(1)<->gamma'(1), martensitic reversible transformations, before and after 100, 200 and 300 thermal cycles.