The waveguiding in thin planar structures with quadratic magneto-optical me
dium is analysed. The permittivity tensor elements with quadratic magneto-o
ptical constants are specified. From synchronous condition for guided modes
in layered system with magnetic ordering the dispersion relation of wavegu
ide is presented. The reflection coefficients for s-polarized light at tran
sversal, longitudinal, and polar configurations as incidence angle function
are described. The influence of quadratic magneto-optical effect on the re
sonant character of the waveguiding term is described in detail. The theory
covers the situation in which the optical response of the structure is lin
ear in the amplitude of the incident wave.