Ferrites, which are used in many microwave devices as circulators or isolators, have complex geometries. When subjected to a magnetic field ferrites exhibit anisotropic and dispersive permeability. If this magnetic field is orthogonal to the direction of propagation the ferrite is characterized by an effective permeability μeff that can be either positive or negative. Many ferrite devices work in a frequency range where μeff is negative. The particular behavior of ferrite in this case is studied in this article with the use of the finite-difference-time-domain (FDTD) method. First phenomena are presented in a one-dimensional case; then a new two-dimensional FDTD algorithm is presented. © 1997 John Wiley & Sons, Inc. Microwave Opt Technol Lett 14: 340–345, 1997.