  We study, both analytically and numerically, disorder-induced localization of
light in random layered structures with magnetooptical materials. The Anderson
localization in such structures demonstrates nonreciprocal features in the
averaged localization length and individual transmission resonances. We employ
short-wavelength approximation where the localization effects are strong, and
consider both the Faraday and Voigt magnetooptical geometries. In the Faraday
geometry, the transmission is strongly nonreciprocal for the circularly
polarized waves, whereas in the Voigt geometry, the nonreciprocity is much
weaker, and it may appear only for the individual transmission resonances of
the TM-polarized waves.
