Abstract The paper reports the effect of one-step and two-step ageing of the [001]-oriented Fe-28Ni-17Co-11.5Al-2.5Nb (FeNiCoAlNb) (at%) single crystals on the precipitate of γ′- and β-phase particles, Ms temperature and reversible deformation under tensile strain, within a wide temperature range from 77 to 373 K. It was shown that during one-step ageing (973 K for 5 h) in FeNiCoAlNb single crystals, γ′-phase particles with L12-type ordering are precipitated. Superelasticity (SE) of 4–5%, associated with the development of γ-α' martensitic transformation (MT) under stress, is realized within the temperature range from 77 to 263 K. Two-step ageing (973К for 5 h and then 873 К for 2 h) results in a structure containing γ′- and β- (with B2-type ordering) phase particles. The precipitation of β-phase particles increases Ms temperature up to 190 K, however, Ms temperature remains below 77 K, when only the γ′-phase is precipitated. In the [001]-oriented crystals with a structure containing γ′- and β-phase particles, a rubber-like behaviour (RLB) of 1.4% at 77 K was found, which was associated with a change in the fine structure of the cooling martensite in the “load-unloading” cycle. For the first time, at tension in the [001]-oriented FeNiCoAlNb crystals with a structure containing two types of particles in the temperature range Ms