Nanostructured samples of Fe - 36% Ni (Invar alloy) and Fe - 50% Ni alloys with a fragment size of about 100 nm were obtained by high pressure torsion using Bridgman anvils. The formation of the nanostructure leads to a decrease in the coefficient of thermal expansion of the Fe - 36% Ni and Fe - 50% Ni alloys by 2.2 and 1.2 times, respectively. Annealing of the Fe - 36% Ni alloy after nanostructuring leads to the formation of a dispersed bcc phase, which is not observed in the coarse-grained Invar alloy. The release of this phase affects the anomalous growth of thermal expansion (above the values typical for a coarse-grained Invar alloy) and the retention of saturation magnetization at temperatures above the Curie temperature of 260 °C. It is found that heating the nanostructured Fe - 50% Ni alloy above the Curie temperature (460 °C) saves the saturation magnetization. By analogy with the results for the Fe - 36% Ni, it can be assumed that this is due to the appearance of a dispersed bcc ferromagnetic phase. Detailed structural analysis will be carried out in future works.