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The effects of inhomogeneous magnetization on optical second harmonic generation from magnetic nanostructures are studied. Cobalt triangular-shaped nanoparticles with vortex magnetization and magnetic trilayers that support the ferromagnetic phase formation are considered. We show that magnetic field dependencies of the SHG intensity for both types of structures reveal a number of distinct peculiarities associated with additional SHG mechanisms attributed to inhomogeneous magnetic state of the nanostructures.