Abstract In the present study the temperature interval of superelasticity in Ti49.4Ni50.6, Co49Ni21Ga30, Ni54Fe19Ga27 and Fe41Ni28Co17Al11.5Ta2.5 (at%) single crystals are investigated. It is shown that it is necessary to produce materials with (i) a high yield stress level of the high-temperature phase of |σcrA| ∼ G/300−G/100 (G is shear modulus), and (ii) a low value of α = d|σcrM|/dT (|σcrM| is the critical stress required for stress-induced martensitic transformation) to achieve high-temperature superelasticity at Т > 373 K. A high stress level of austenite |σcrA| can be obtained through selection of the crystal axis orientation, the stress state (tension vs. compression), variation of the chemical composition of the intermetallic compounds, and precipitation of dispersed particles. Low values of α are realized for crystal orientations providing maximum values for the transformation strain |ɛ0|.