This paper concerns the investigation of the critical (HC) and the saturation (HS) magnetic fields behavior of the studied system as a function of different physical parameters. The Monte Carlo method has been used to study the magnetic properties of a ferrimagnetic behavior of a double fullerene X60 core/shell like-nanostructure, where the symbol X can be assigned to any magnetic atom. Based on the Ising model, we focus our study on a system formed by a double sphere core/shell. The two spheres are containing the spins: $\sigma=\pm 1/2$ in the core are surrounded by the spin $S=\pm 1, 0$ in the shell. Many types of magnetization curves have been found, depending on the competitions among the exchange couplings, the crystal fields and the temperature.
