Thermoelastic martensitic transformations (MT) during cooling/heating and under loading give rise to functional properties such as the shape memory effect and superelasticity [1][2][3][4]. Fe -28% Ni -17% Co -11.5% Al -2.5% Ta -0.05% B (at.%) disordered iron-based alloys suggested by Y. Tanaka et al. in 2010 [5] have high strength, anomalously high superelasticity (of the order of 13%) caused by the γ-α′ MT under loading, good plasticity, and high damping ability in the polycrystalline state. High strength with anomalously high superelasticity of these alloys is reached due to precipitation of disperse γ′-phase particles [5]. Hardening of the γ-phase by disperse particles leads to the suppression of the plastic flow processes during the γ-α′ MT. The disperse γ′ particles undergo no MT, facilitate the accumulation of elastic energy in martensitic crystals, and change the degree of α′-martensite tetragonality; as a result, the volume change ΔV γ-α′ during MT is ≤1%. This is conventionally reached by precipitation of small disperse particles with sizes d < 10 nm [2,5].This work presents for the first time results of investigations into the development of thermoelastic γ-α′ MT in Fe -28% Ni -17% Co -11.5% Al -2.5 % Ta (at.%) single crystals. These investigations are necessary because of the following circumstances. First, single crystals give unique possibility to suppress the development of intermittent decomposition of polycrystals on grain boundaries caused by precipitation of the fragile intermetallic phase. Second, a comparison of data obtained for single and polycrystals of these alloys will allow the role of grains in the development of thermoelastic transformations to be elucidated.Single crystals of the Fe -28% Ni -17% Co -11.5% Al -2.5% Ta (at.%) alloy were grown from magnesium oxide in crucibles by the Bridgeman method in a helium atmosphere. They were aged at Т = 973 K for t = 0-25 h with subsequent water quenching. Temperatures of the γ-α′ MT were determined from bends of the curve showing the temperature dependence of the electrical resistance. Figure 1 shows the temperature dependence of the electrical resistance ρ(T) for crystals after quenching and aging at Т = 973 K. In the quenched state, no stages characteristic of the MT development are seen in the curve ρ(T) for these alloys, and ρ is independent of the temperature (curve 1 in Fig. 1) [2]. Aging at Т = 973 K for t = 7, 10, 15, and 20 h leads to the occurrence of stages in the curves ρ(T) (curves 2-5 in Fig. 1). According to [2], the temperature at which ρ(T) decreases corresponds to the temperature M s at which the MT is started during cooling, and the temperature at which the stage of fast decrease of the electrical resistance terminates corresponds to the temperature M f at which the direct MT is finished. During heating at temperature A s at which the inverse MT is started, the fast increase of ρ(T) is observed, and at Т = A f at which the inverse MT is finished, the fast increase of the electrical resistance is terminated. An analysis of cu...