The reversible thermoelastic γ-α′ martensitic transformations under load in new single-crystal ferromagnetic Fe-28%Ni-17%Co-11.5%Al-2.5%Ti (at %) alloy have been studied. It is shown for the first time that precipitation of dispersed particles of the γ′ phase during aging for 7 h at 973 K induces the shape-memory effect and superelasticity in [001] single crystals of Fe-Ni-Co-Al-Ti alloy upon tensile strain. Superelasticity ɛ_SE = 4.5–6% manifests itself in the temperature range T = 183–333 K.