The magnetic structure, nonequilibrium and equilibrium states, and magnetic inhomogeneities of austenite in invar Fe–Ni alloys are analysed to substantiate the possibility of the existence of concentration inhomogeneities with a disoriented magnetic structure, which can be the centres of the magnetic $\gamma$$\leftrightarrow$$\alpha$-transition of the first kind. The results of the considered experimental and theoretical studies of this system are summarised. As shown, the magnetic structure and non-equilibrium state of austenite alone cannot lead to the appearance of concentration (magnetic) inhomogeneities in invar alloys. As assumed, the existing concentration inhomogeneities are of fluctuation origin. A model is proposed that explains the basic invar properties of Fe–Ni alloys by the existence of the original magnetic structure of austenite and its inhomogeneous and non-equilibrium state relative to the $\alpha$-phase. It assumes that concentration inhomogeneities with a disoriented magnetic structure in the austenite of invar Fe–Ni alloys in a wide temperature range, from the Curie point to the martensitic point, can play the role of compressed elastic elements in the interior of the ferromagnetic $\gamma$-phase. In fact, they are the subcritical nuclei of $\alpha$-martensite of the first kind magnetic phase transition. Abnormally large changes in the volume of invar Fe–Ni alloys occur as a result of the combined action of a thermodynamic stimulus in the $\gamma$-phase, whose volume is ‘pushed’ to grow by numerous areas of inhomogeneities (subcritical nuclei of the $\alpha$ phase), and changes in its magnetisation in a strong magnetic field and/or during cooling due to the ordering of atomic magnetic moments.