Alloys of the Fe-Ni system have found a wide application in modern technology and instrument making. One of the most famous Fe-Ni alloys is Invar alloy (with a Ni content of 36 wt.%), which has a low coefficient of thermal expansion. A significant drawback of this alloy is its low strength and hardness, which limits its use. In this work, a strong Invar alloy was obtained by severe plastic deformation by high pressure torsion using Bridgman anvils. The microstructure of the Invar 36 alloy after nanostructuring was represented by fragments with an average size of about 100 nm. Thermal analysis of nanostructured Invar showed that the curves recorded in the differential scanning calorimetry mode show endothermic and exothermic peaks. This peak indicates a phase transformation in the nanostructured alloy. The assessment of the strength properties is carried out by measuring the microhardness by the Vickers method. The value of the microhardness of the alloy Invar 36 in the nanostructured state is twice higher than in the coarse-grained state. However, on the curves of microhardness dependence on annealing temperature, a maximum is observed after annealing of nanostructured Invar in the temperature range from 380 to 450°C associated with the precipitation hardening due to the formation of a nanosized bcc phase that is not observed in the coarse-grained Invar alloy. An increase in the annealing temperature above 450°C leads to a decrease of microhardness as a result of two processes -recrystallization of the grains and dissolution of the bcc phase. Anomalous precipitation of the bcc phase in the nanostructured Invar alloy became possible due to an increase of diffusion capacity due to the formation of nonequilibrium, highly defected structure after deformational nanostructuring.