The regularities of the grain structure formation of the austenitic phase in the ribbon of the metastable iron-nickel alloy Fe-31.4% wt. Ni-0.05% wt. C, formed in the conditions of high temperature gradients during quenching from the melt and its influence on the realization of martensitic γ-αtransformation in the local regions of the formed ribbon are investigated. The dependence of the completeness of the martensitic transformation and morphology of martensite crystals on the grain size of austenite is analysed. The change in the relative intensity of the diffraction reflexes of the γ-phase lines along the depth of the ribbon is characterized by a continuous change in the degree of austenite texture. The consequences of the influence of relaxation processes during the crystallization of the ribbon on the value of residual stresses, the presence of triple 120° joints between the grains as signs of equilibrium, and the change in their number along the ribbon are investigated.