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Using the methods of electron microscopy and X-ray analysis in combination with measurements of the electrical resistance and magnetic susceptibility, the authors have obtained data on the peculiar features of pre-martensitic states and martensitic transformations, as well as subsequent decomposition, in the alloys with shape memory effect of Cu–14wt%Al–3wt%Ni and Cu–13.5wt%Al–3.5wt%Ni. For the first time, we established the microstructure, phase composition, mechanical properties, and microhardness of the alloys obtained in the nanocrystalline state as a result of severe plastic deformation under high pressure torsion and subsequent annealing. A crystallographic model of the martensite nucleation and the rearrangements β1→β1' and β1→γ1ꞌ are proposed based on the analysis of the observed tweed contrast and diffuse scattering in the austenite and the internal defects in the substructure of the martensite.