Within the model of two-phase (core/shell) ellipsoidal nanoparticles, the effects of the interfacial exchange interaction, size, elongation, and orientation of the major axes of the core and shell on the meta-stability of magnetic states have been simulated. Using the example of Fe2.44Ti0.56O4 nanoparticles,Fe3O4 it is shown that the metastability of magnetic states is realized in a limited range of the constant of interfacial exchange interaction between the core and shell, Ain , and geometric parameters. With an increase in the absolute value of the interfacial exchange interaction constant, , from Ain = 0 to some finite value, theAin metastability of magnetic states decreases monotonically from maximum to zero, regardless of the angle between the major axes of the core and the shell.