Using single crystals of the Ni₄₉Fe₁₈Ga₂₇Co₆ (at.%) alloy, oriented along [001]- and [123]-directions, cyclic stability of superelasticity is investigated in isothermal loading/unloading cycles at T = A_f +(12–15) K (100 cycles) under compressive stress as a function of given strain per cycle, presence of disperse γ-phase particles measuring 5–10 μm, austenitic (B2 or L2₁) and stress-induced martensitic crystal structure (14M or L10). It is shown that single-phase L2₁-crystals demonstrate high cyclic stability during L21–14M-transitions with narrow hysteresises Δσ < 50 MPa in the absence of detwinning of the martensite. During the development of L2₁–14M stress-induced transformation, the reversible energy ΔGrev for these crystals exceeds the dissipated energy ΔG_irr, and ΔG_rev/ΔG_irr = 1.7–1.8. A significant degradation of superelasticity is observed in [123]-oriented crystals during the development of L2₁–14M–L1₀-transformations followed by detwinning of the L10-martensite crystals and heterophase (B2+γ) single crystals, irrespective of their orientation during the B2–L10-transition. In the latter case, martensitic transformations are characterized by a wide stress hysteresis Δσ ≥ 80 MPa and the dissipated energy exceeds the reversible energy ΔG_rev/ΔG_irr = 0.5. The empirical criterion, relying on the analysis of the reversible-to-irreversible energy ratio, ΔG_rev/ΔG_irr, during stressinduced martensitic transformations, can be used to predict the cyclic stability of superelasticity in NiFeGaCo alloys subjected to different types of heat treatment.