Abstract: The guidance conditions of a slab waveguide of uniaxially anisotropic metamaterial with partially negative components in permittivity and permeability tensors are derived. In terms of the combination of component signs, the even mode properties for guided TE waves are discussed in different cases. The Brillouin diagrams with real transverse wave numbers inside a slab waveguide are drawn. The results show that under some specific conditions there are infinite guided modes, which is different from the case in the traditional dielectric waveguide and isotropic metamaterial slab where only finite number of guided modes exists. It is also found that there are multiple solutions of the propagating mode with imaginary transverse wave number for certain component parameters, and the mode has the h