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Magnetooptical properties of one-dimensional aperiodic structures formed by stacking together magnetic and nonmagnetic layers according to the Kolakoski self-generation scheme are studied theoretically using the 4x4 transfer matrix method. The effect of the generation stage of the sequence, and the helicity and direction of light propagation through the magneto-photonic crystals on the transmission/reflection spectra as well as Faraday and ellipticity rotations, have been investigated. Our results reveal that this kind of aperiodic magneto-photonic crystals can be used for the fabrication of multifrequency laser cavities, and optical filters/sensors.