The influence of chemical composition on the phase composition, stability, and type of crystal structure of austenitic and martensitic phases of triple alloys of quasi-binary NiMn-NiTi cut is analyzed. The temperature and concentration conditions of their existence are determined. It is established that titanium alloying decreases the critical temperatures of thermoelastic martensitic transformations in alloys compared to the basic binary intermetallic NiMn alloy. The phase decomposition is revealed in alloys alloyed with more than 15 at.% titanium with precipitations of three-component 4H-HCP (Ni3Ti) enriched by titanium in comparison with the B2 matrix and the Widmannstätten substructure.