We report on significant enhancement of the magnetooptical effects in gyrotropic systems of a metallic film perforated by subwavelength hole arrays and a uniform dielectric film magnetized perpendicular to its plane. Calculations, based on a rigorous coupled-wave analysis, demonstrate the Faraday and Kerr effect spectra having several resonance peaks in the near infrared range, some of them coinciding with transmittance peaks. Qualitative analysis revealed that magnetic polaritons being coupled magnetic-film waveguiding modes with surface plasmons play a crucial role in the observed effect. At the same time, substantial MO effect enhancement can be achieved in some nanostructured materials owing to the materials' interesting optical properties inherent to their nanoscaled