The work is devoted to a study of the structure and mechanical properties of two nonequiatomic medium-entropy nanocrystalline alloys, in which in a coarse state additional mechanisms act during plastic deformation — twinning (TWIP) in the Fe40Mn40Co10Cr10 alloy and phase transformations (TRIP) in the Fe50Mn30Co10Cr10 alloy. The nanocrystalline state in these alloys is achieved by high-pressure torsion (HPT) at 300 K and 77 K after different numbers of revolutions n = 0.25 and 5. In the nanostructural state in the TWIP Fe40Mn40Co10Cr10 and the TRIP Fe50Mn30Co10Cr10 alloys, a basically complete phase transition from the fcc lattice to hcp is observed, the content of which does not depend very strongly on the HPT temperature and deformation. For both alloys in the nanostructured state, there is a significant decrease in differences in the phase composition and microhardness Hv by comparison with the coarse-grained state. A decrease in the HPT temperature and an increase in HPT deformation for all the cases studied lead to an increase in the value of Hv. The Fe40Mn40Co10Cr10 TWIP alloy remains ductile under active compression deformation at 300 and 77 K, while there is no macroscopic plasticity in the Fe50Mn30Co10Cr10 TRIP alloy under similar conditions. For the Fe40Mn40Co10Cr10 TWIP the thermally-activated character of plastic deformation is retained during the transition from the coarse-grained to the nanostructured state.