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Anisotropy of the nonlinear magnetooptical (MO) response in regular arrays of Py antidots and «С»-, «U»- and «O»- shaped Py nanoelements is studied by means of the MO Kerr effect at the second harmonic (SH) wavelength. We demonstrate that the values of the MO effect and coercivity depend substantially on the azimuthal orientation of the antidots array relatively to the external magnetic field. In the arrays of «С»-, «U»- and «O»- shaped Py nanoelements the circular dichroism (CD) of the SH response was observed due to the extrinsic chirality of the samples. We demonstrate that the averaged over the azimuthal angle value of the CD depends on the applied to the structure magnetic field.