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The parallel-polarized surface waves which propagate on a planar ferrite slab are considered. The ferrite material is isotropic and homogeneous, the slab rests on a perfectly conducting ground plane, and the ambient medium is free space. Only one mode can propagate on a thin lossless slab, but more and more of the higher order modes begin to propagate when one increases the thickness or the loss tangent of the slab. As the thickness and the loss are increased, the lowest order mode takes on the properties of the Zenneck wave. At the same time, the higher order modes take on the properties of a homogeneous plane wave propagating in the grazing direction in the slab. Among the most interesting properties of a surface wave are the attenuation constant and the phase velocity. Contour maps are included to show how these quantities depend on the thickness, permittivity, permeability and loss tangents of the ferrite slab. Additional insight is provided by graphs showing the root trajectories, cutoff boundaries and field distributions of the four lowest order surface-wave modes.