In this paper, we show through a numerical investigation that an anisotropic self-complementary metasurface constituted by a sequence of capacitive and inductive strips supports at low frequency two degenerate quasi TE- and TM surface-waves modes with identical dispersion characteristics. It is also seen that group velocity drastically changes depending on the direction of propagation of the surface waves, becoming extremely low for the direction of propagation orthogonal to the strips. The phenomenon can be used in dual-polarized leaky-wave antennas.